Subgroups — C₁₉×#62327 #18068286

Order 4864.

1812 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3551	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3337	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3327	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3322	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3282	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3256	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3203	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3202	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3199	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#3168	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3060	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3057	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#135	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
16	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#563	—	2	2	no	—
19	C₁₉×#560	—	2	2	no	—
20	C₁₉×#555	—	2	2	no	—
21	C₁₉×#553	C₂²	1	4	yes	—
22	C₁₉×#552	C₂²	1	4	yes	complemented
23	C₁₉×#551	—	2	2	no	—
24	C₁₉×#548	C₂²	1	4	yes	—
25	C₁₉×#546	C₂²	1	4	yes	complemented
26	C₁₉×#540	—	2	4	no	—
27	C₁₉×#538	—	2	4	no	—
28	C₁₉×#537	C₂²	1	4	yes	complemented
29	C₁₉×#536	C₂²	1	2	yes	—
30	C₁₉×#535	C₂²	1	2	yes	—
31	C₁₉×#532	C₂²	1	1	yes	characteristic
32	C₁₉×#529	C₂²	1	4	yes	complemented
33	C₁₉×#499	C₂²	1	2	yes	complemented
34	C₁₉×#495	C₂²	1	2	yes	—
35	C₁₉×#488	C₂²	1	4	yes	complemented
36	C₁₉×#485	C₂²	1	4	yes	complemented
37	C₁₉×#484	C₂²	1	4	yes	complemented
38	C₁₉×#482	C₂²	1	4	yes	—
39	C₁₉×#480	C₂²	1	4	yes	complemented
40	C₁₉×#479	C₂²	1	4	yes	complemented
41	C₁₉×#478	C₂²	1	4	yes	complemented
42	C₁₉×#470	C₂²	1	2	yes	complemented
43	C₁₉×#470	C₂²	1	2	yes	complemented
44	C₁₉×#469	C₂²	1	2	yes	—
45	C₁₉×#469	C₂²	1	2	yes	—
46	C₁₉×#468	C₂²	1	4	yes	—
47	C₁₉×#468	C₂²	1	4	yes	complemented
48	C₁₉×#467	C₂²	1	2	yes	complemented
49	C₁₉×#466	C₂²	1	2	yes	—
50	C₁₉×#465	C₂²	1	4	yes	—
51	C₁₉×#465	C₂²	1	4	yes	complemented
52	C₁₉×#465	C₂²	1	4	yes	complemented
53	C₁₉×#464	C₂²	1	4	yes	complemented
54	C₁₉×#463	C₂²	1	4	yes	—
55	C₁₉×#452	C₂²	1	4	yes	complemented
56	C₁₉×#451	C₂²	1	4	yes	complemented
57	C₁₉×#449	C₂²	1	4	yes	—
58	C₁₉×#447	C₂²	1	4	yes	—
59	C₄×Q₁₆×C₁₉	C₂²	1	2	yes	complemented
60	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
61	C₄×D₈×C₁₉	C₂²	1	2	yes	—
62	C₁₉×#436	C₂²	1	4	yes	complemented
63	C₈×D₄×C₁₉	C₂²	1	4	yes	complemented
64	C₁₉×#427	C₂²	1	2	yes	complemented
65	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
66	C₁₉×#423	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#419	C₂²	1	2	yes	complemented
68	C₁₉×#418	C₂²	1	2	yes	complemented
69	C₁₉×#417	C₂²	1	4	yes	complemented
70	C₁₉×#408	C₂²	1	1	yes	characteristic
71	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
73	C₂×#41×C₁₉	C₂³	1	4	yes	—
74	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
78	C₁₉×#135	—	4	4	no	—
79	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
80	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
81	C₂×SD₁₆×C₁₉	—	4	4	no	—
82	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
83	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
84	C₂×D₈×C₁₉	C₂³	1	2	yes	—
85	C₂×D₈×C₁₉	C₂³	1	2	yes	—
86	C₁₉×#131	—	4	2	no	—
87	C₁₉×#131	—	4	2	no	—
88	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
91	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
95	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×C₄⋊Q₈	—	2	2	no	—
97	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
98	C₁₉×#127	—	2	2	no	—
99	C₁₉×#127	D₄	1	1	yes	characteristic
100	C₁₉×#126	—	2	4	no	—
101	C₁₉×#126	—	2	4	no	—
102	C₁₉×#126	—	2	4	no	—
103	C₁₉×#125	—	2	4	no	—
104	C₁₉×#125	C₂³	1	4	yes	—
105	C₁₉×#124	—	2	2	no	—
106	C₁₉×#124	—	2	2	no	—
107	C₁₉×#124	—	2	4	no	—
108	C₁₉×#124	D₄	1	1	yes	characteristic
109	C₁₉×#124	D₄	1	1	yes	characteristic
110	C₁₉×#124	C₂³	1	4	yes	—
111	C₁₉×#123	—	2	2	no	—
112	C₁₉×#123	—	2	2	no	—
113	C₁₉×#123	—	2	4	no	—
114	C₁₉×#123	—	2	4	no	—
115	C₁₉×#123	—	2	4	no	—
116	C₁₉×#123	—	2	4	no	—
117	C₁₉×C₂²⋊Q₈	—	2	4	no	—
118	C₁₉×C₂²⋊Q₈	—	2	4	no	—
119	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
120	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
121	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
122	C₁₉×#121	—	2	4	no	—
123	C₁₉×#121	—	2	4	no	—
124	C₁₉×#121	—	2	4	no	—
125	C₁₉×#121	—	2	4	no	—
126	C₁₉×#121	—	2	4	no	—
127	C₁₉×#121	—	2	4	no	—
128	C₁₉×#121	D₄	1	4	yes	—
129	C₁₉×#121	C₂³	1	4	yes	—
130	C₁₉×#121	C₂³	1	4	yes	—
131	C₁₉×#121	C₂³	1	4	yes	—
132	C₁₉×#120	—	2	2	no	—
133	C₁₉×#120	—	2	2	no	—
134	C₁₉×#120	—	2	4	no	—
135	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
136	C₄×D₄×C₁₉	—	2	4	no	—
137	C₄×D₄×C₁₉	—	2	4	no	—
138	C₄×D₄×C₁₉	—	2	4	no	—
139	C₄×D₄×C₁₉	C₂³	1	4	yes	—
140	C₄×D₄×C₁₉	C₂³	1	4	yes	—
141	C₁₉×#117	—	2	4	no	—
142	C₁₉×#117	—	2	4	no	—
143	C₁₉×#117	C₂³	1	2	yes	—
144	C₁₉×#117	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
148	C₁₉×#107	C₂³	1	4	yes	—
149	C₁₉×#107	C₂³	1	2	yes	—
150	C₁₉×#107	C₂³	1	2	yes	—
151	C₁₉×#106	C₂³	1	4	yes	—
152	C₁₉×#106	C₂³	1	2	yes	—
153	C₁₉×#106	C₂³	1	2	yes	—
154	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
155	C₁₉×#103	C₂³	1	4	yes	—
156	C₁₉×#103	C₂³	1	4	yes	—
157	C₁₉×#103	C₂³	1	4	yes	—
158	C₁₉×#103	C₂³	1	4	yes	—
159	C₁₉×#102	C₂³	1	4	yes	—
160	C₁₉×#102	C₂³	1	4	yes	—
161	C₁₉×#102	C₂³	1	4	yes	—
162	C₁₉×#102	C₂³	1	4	yes	—
163	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
165	C₄×C₈×C₁₉	C₂³	1	2	yes	—
166	C₄×C₈×C₁₉	C₂³	1	2	yes	—
167	C₂⁴×C₁₉	—	2	2	no	—
168	#41×C₁₉	—	4	1	no	—
169	#41×C₁₉	—	4	1	no	—
170	#41×C₁₉	—	4	1	no	—
171	#41×C₁₉	—	4	1	no	—
172	#41×C₁₉	—	4	4	no	—
173	#41×C₁₉	—	4	4	no	—
174	C₂×Q₈×C₁₉	—	2	2	no	—
175	C₂×Q₈×C₁₉	—	4	2	no	—
176	C₂×Q₈×C₁₉	—	4	2	no	—
177	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
179	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
180	C₂×D₄×C₁₉	—	2	4	no	—
181	C₂×D₄×C₁₉	—	2	4	no	—
182	C₂×D₄×C₁₉	—	2	4	no	—
183	C₂×D₄×C₁₉	—	2	4	no	—
184	C₂×D₄×C₁₉	—	2	2	no	—
185	C₂×D₄×C₁₉	—	4	2	no	—
186	C₂×D₄×C₁₉	—	4	2	no	—
187	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
188	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
190	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
191	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
192	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₉	—	2	4	no	—
194	C₂²×C₄×C₁₉	—	2	2	no	—
195	C₂²×C₄×C₁₉	—	2	4	no	—
196	C₂²×C₄×C₁₉	—	2	4	no	—
197	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
201	Q₁₆×C₁₉	—	4	2	no	—
202	Q₁₆×C₁₉	—	4	2	no	—
203	SD₁₆×C₁₉	—	2	8	no	—
204	SD₁₆×C₁₉	—	4	4	no	—
205	D₈×C₁₉	—	4	2	no	—
206	D₈×C₁₉	—	4	2	no	—
207	M₁₆×C₁₉	—	4	2	no	—
208	M₁₆×C₁₉	—	4	2	no	—
209	M₁₆×C₁₉	—	4	1	no	—
210	M₁₆×C₁₉	—	4	1	no	—
211	C₂×C₈×C₁₉	—	2	2	no	—
212	C₂×C₈×C₁₉	—	2	4	no	—
213	C₂×C₈×C₁₉	—	2	4	no	—
214	C₂×C₈×C₁₉	—	4	1	no	—
215	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
216	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
217	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
218	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
219	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
220	C₄⋊C₄×C₁₉	—	2	4	no	—
221	C₄⋊C₄×C₁₉	—	2	4	no	—
222	C₄⋊C₄×C₁₉	—	2	4	no	—
223	C₄⋊C₄×C₁₉	—	2	4	no	—
224	C₄⋊C₄×C₁₉	—	2	4	no	—
225	C₄⋊C₄×C₁₉	—	2	4	no	—
226	C₄⋊C₄×C₁₉	—	2	4	no	—
227	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
228	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
229	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
230	C₂²⋊C₄×C₁₉	—	2	4	no	—
231	C₂²⋊C₄×C₁₉	—	2	4	no	—
232	C₂²⋊C₄×C₁₉	—	2	2	no	—
233	C₂²⋊C₄×C₁₉	—	2	2	no	—
234	C₂²⋊C₄×C₁₉	—	2	4	no	—
235	C₂²⋊C₄×C₁₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₉	—	2	4	no	—
237	C₂²⋊C₄×C₁₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₉	—	2	4	no	—
240	C₂²⋊C₄×C₁₉	—	2	4	no	—
241	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
242	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
243	C₄²×C₁₉	—	2	2	no	—
244	C₄²×C₁₉	—	2	4	no	—
245	C₄²×C₁₉	—	2	2	no	—
246	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
247	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
248	C₄²×C₁₉	C₂⁴	1	2	yes	—
249	#62327	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₁₉	—	2	4	no	—
251	C₂³×C₁₉	—	8	2	no	—
252	C₂³×C₁₉	—	8	4	no	—
253	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
254	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
256	Q₈×C₁₉	—	2	4	no	—
257	Q₈×C₁₉	—	2	4	no	—
258	Q₈×C₁₉	—	4	1	no	—
259	Q₈×C₁₉	—	4	1	no	—
260	Q₈×C₁₉	—	8	2	no	—
261	D₄×C₁₉	—	2	4	no	—
262	D₄×C₁₉	—	2	4	no	—
263	D₄×C₁₉	—	4	4	no	—
264	D₄×C₁₉	—	4	2	no	—
265	D₄×C₁₉	—	4	1	no	—
266	D₄×C₁₉	—	4	1	no	—
267	D₄×C₁₉	—	4	2	no	—
268	D₄×C₁₉	—	8	2	no	—
269	D₄×C₁₉	—	8	4	no	—
270	D₄×C₁₉	—	8	4	no	—
271	D₄×C₁₉	—	8	4	no	—
272	D₄×C₁₉	—	8	4	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	2	2	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	1	no	—
277	C₂×C₄×C₁₉	—	2	2	no	—
278	C₂×C₄×C₁₉	—	2	2	no	—
279	C₂×C₄×C₁₉	—	2	4	no	—
280	C₂×C₄×C₁₉	—	2	4	no	—
281	C₂×C₄×C₁₉	—	2	4	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	—	8	4	no	—
284	C₂×C₄×C₁₉	—	8	4	no	—
285	C₂×C₄×C₁₉	—	8	4	no	—
286	C₂×C₄×C₁₉	—	8	2	no	—
287	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
293	C₈×C₁₉	—	2	1	no	—
294	C₈×C₁₉	—	2	2	no	—
295	C₈×C₁₉	—	2	2	no	—
296	C₈×C₁₉	—	2	2	no	—
297	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
298	#3551	C₂×C₁₉	1	2	yes	complemented
299	#3337	C₂×C₁₉	1	4	yes	complemented
300	#3327	C₂×C₁₉	1	4	yes	complemented
301	#3322	C₂×C₁₉	1	4	yes	complemented
302	#3282	C₂×C₁₉	1	4	yes	complemented
303	#3256	C₂×C₁₉	1	2	yes	complemented
304	#3203	C₂×C₁₉	1	2	yes	complemented
305	#3202	C₂×C₁₉	1	1	yes	characteristic, complemented
306	#3199	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#3168	C₂×C₁₉	1	2	yes	complemented
308	#3060	C₂×C₁₉	1	2	yes	complemented
309	#3057	C₂×C₁₉	1	2	yes	complemented
310	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
311	C₂²×C₁₉	—	2	2	no	—
312	C₂²×C₁₉	—	2	4	no	—
313	C₂²×C₁₉	—	2	4	no	—
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	2	1	no	—
316	C₂²×C₁₉	—	2	2	no	—
317	C₂²×C₁₉	—	4	4	no	—
318	C₂²×C₁₉	—	4	4	no	—
319	C₂²×C₁₉	—	4	4	no	—
320	C₂²×C₁₉	—	16	4	no	—
321	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
322	C₄×C₁₉	—	2	2	no	—
323	C₄×C₁₉	—	2	2	no	—
324	C₄×C₁₉	—	2	2	no	—
325	C₄×C₁₉	—	2	1	no	—
326	C₄×C₁₉	—	2	2	no	—
327	C₄×C₁₉	—	4	4	no	—
328	C₄×C₁₉	—	4	4	no	—
329	C₄×C₁₉	—	4	4	no	—
330	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
331	C₄×C₁₉	#585	1	1	yes	characteristic
332	C₂×#135	C₂²×C₁₉	1	2	yes	—
333	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
334	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
335	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
336	#563	—	2	2	no	—
337	#560	—	2	2	no	—
338	#555	—	2	2	no	—
339	#553	C₂²×C₁₉	1	4	yes	—
340	#552	C₂²×C₁₉	1	4	yes	complemented
341	#551	—	2	2	no	—
342	#548	C₂²×C₁₉	1	4	yes	—
343	#546	C₂²×C₁₉	1	4	yes	complemented
344	#540	—	2	4	no	—
345	#538	—	2	4	no	—
346	#537	C₂²×C₁₉	1	4	yes	complemented
347	#536	C₂²×C₁₉	1	2	yes	—
348	#535	C₂²×C₁₉	1	2	yes	—
349	#532	C₂²×C₁₉	1	1	yes	characteristic
350	#529	C₂²×C₁₉	1	4	yes	complemented
351	#499	C₂²×C₁₉	1	2	yes	complemented
352	#495	C₂²×C₁₉	1	2	yes	—
353	#488	C₂²×C₁₉	1	4	yes	complemented
354	#485	C₂²×C₁₉	1	4	yes	complemented
355	#484	C₂²×C₁₉	1	4	yes	complemented
356	#482	C₂²×C₁₉	1	4	yes	—
357	#480	C₂²×C₁₉	1	4	yes	complemented
358	#479	C₂²×C₁₉	1	4	yes	complemented
359	#478	C₂²×C₁₉	1	4	yes	complemented
360	#470	C₂²×C₁₉	1	2	yes	complemented
361	#470	C₂²×C₁₉	1	2	yes	complemented
362	#469	C₂²×C₁₉	1	2	yes	—
363	#469	C₂²×C₁₉	1	2	yes	—
364	#468	C₂²×C₁₉	1	4	yes	—
365	#468	C₂²×C₁₉	1	4	yes	complemented
366	#467	C₂²×C₁₉	1	2	yes	complemented
367	#466	C₂²×C₁₉	1	2	yes	—
368	#465	C₂²×C₁₉	1	4	yes	—
369	#465	C₂²×C₁₉	1	4	yes	complemented
370	#465	C₂²×C₁₉	1	4	yes	complemented
371	#464	C₂²×C₁₉	1	4	yes	complemented
372	#463	C₂²×C₁₉	1	4	yes	—
373	#452	C₂²×C₁₉	1	4	yes	complemented
374	#451	C₂²×C₁₉	1	4	yes	complemented
375	#449	C₂²×C₁₉	1	4	yes	—
376	#447	C₂²×C₁₉	1	4	yes	—
377	C₄×Q₁₆	C₂²×C₁₉	1	2	yes	complemented
378	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
379	C₄×D₈	C₂²×C₁₉	1	2	yes	—
380	#436	C₂²×C₁₉	1	4	yes	complemented
381	C₈×D₄	C₂²×C₁₉	1	4	yes	complemented
382	#427	C₂²×C₁₉	1	2	yes	complemented
383	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
384	#423	C₂²×C₁₉	1	1	yes	characteristic, complemented
385	#419	C₂²×C₁₉	1	2	yes	complemented
386	#418	C₂²×C₁₉	1	2	yes	complemented
387	#417	C₂²×C₁₉	1	4	yes	complemented
388	#408	C₂²×C₁₉	1	1	yes	characteristic
389	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
390	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
391	C₂×C₁₉	—	4	1	no	—
392	C₂×C₁₉	—	4	2	no	—
393	C₂×C₁₉	—	4	2	no	—
394	C₂×C₁₉	—	8	4	no	—
395	C₂×C₁₉	#3496	1	1	yes	characteristic
396	C₂×C₁₉	#3584	1	2	yes	—
397	C₂×#41	C₂³×C₁₉	1	4	yes	—
398	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
399	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
400	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
401	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
402	#135	—	4	4	no	—
403	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
404	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
405	C₂×SD₁₆	—	4	4	no	—
406	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
407	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
408	C₂×D₈	C₂³×C₁₉	1	2	yes	—
409	C₂×D₈	C₂³×C₁₉	1	2	yes	—
410	#131	—	4	2	no	—
411	#131	—	4	2	no	—
412	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
413	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
414	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
415	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
416	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
418	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
419	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
420	C₄⋊Q₈	—	2	2	no	—
421	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
422	#127	—	2	2	no	—
423	#127	D₄×C₁₉	1	1	yes	characteristic
424	#126	—	2	4	no	—
425	#126	—	2	4	no	—
426	#126	—	2	4	no	—
427	#125	—	2	4	no	—
428	#125	C₂³×C₁₉	1	4	yes	—
429	#124	—	2	2	no	—
430	#124	—	2	2	no	—
431	#124	—	2	4	no	—
432	#124	D₄×C₁₉	1	1	yes	characteristic
433	#124	D₄×C₁₉	1	1	yes	characteristic
434	#124	C₂³×C₁₉	1	4	yes	—
435	#123	—	2	2	no	—
436	#123	—	2	2	no	—
437	#123	—	2	4	no	—
438	#123	—	2	4	no	—
439	#123	—	2	4	no	—
440	#123	—	2	4	no	—
441	C₂²⋊Q₈	—	2	4	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
444	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
445	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
446	#121	—	2	4	no	—
447	#121	—	2	4	no	—
448	#121	—	2	4	no	—
449	#121	—	2	4	no	—
450	#121	—	2	4	no	—
451	#121	—	2	4	no	—
452	#121	D₄×C₁₉	1	4	yes	—
453	#121	C₂³×C₁₉	1	4	yes	—
454	#121	C₂³×C₁₉	1	4	yes	—
455	#121	C₂³×C₁₉	1	4	yes	—
456	#120	—	2	2	no	—
457	#120	—	2	2	no	—
458	#120	—	2	4	no	—
459	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
460	C₄×D₄	—	2	4	no	—
461	C₄×D₄	—	2	4	no	—
462	C₄×D₄	—	2	4	no	—
463	C₄×D₄	C₂³×C₁₉	1	4	yes	—
464	C₄×D₄	C₂³×C₁₉	1	4	yes	—
465	#117	—	2	4	no	—
466	#117	—	2	4	no	—
467	#117	C₂³×C₁₉	1	2	yes	—
468	#117	C₂³×C₁₉	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
470	C₂×C₂²⋊C₄	—	2	4	no	—
471	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
472	#107	C₂³×C₁₉	1	4	yes	—
473	#107	C₂³×C₁₉	1	2	yes	—
474	#107	C₂³×C₁₉	1	2	yes	—
475	#106	C₂³×C₁₉	1	4	yes	—
476	#106	C₂³×C₁₉	1	2	yes	—
477	#106	C₂³×C₁₉	1	2	yes	—
478	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
479	#103	C₂³×C₁₉	1	4	yes	—
480	#103	C₂³×C₁₉	1	4	yes	—
481	#103	C₂³×C₁₉	1	4	yes	—
482	#103	C₂³×C₁₉	1	4	yes	—
483	#102	C₂³×C₁₉	1	4	yes	—
484	#102	C₂³×C₁₉	1	4	yes	—
485	#102	C₂³×C₁₉	1	4	yes	—
486	#102	C₂³×C₁₉	1	4	yes	—
487	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
488	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
489	C₄×C₈	C₂³×C₁₉	1	2	yes	—
490	C₄×C₈	C₂³×C₁₉	1	2	yes	—
491	C₁₉	#62327	1	1	yes	characteristic, direct product factor, Sylow
492	C₂⁴	—	2	2	no	—
493	#41	—	4	1	no	—
494	#41	—	4	1	no	—
495	#41	—	4	1	no	—
496	#41	—	4	1	no	—
497	#41	—	4	4	no	—
498	#41	—	4	4	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	4	2	no	—
501	C₂×Q₈	—	4	2	no	—
502	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
503	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
504	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	4	2	no	—
511	C₂×D₄	—	4	2	no	—
512	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
513	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
514	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
515	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
516	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
526	Q₁₆	—	4	2	no	—
527	Q₁₆	—	4	2	no	—
528	SD₁₆	—	2	8	no	—
529	SD₁₆	—	4	4	no	—
530	D₈	—	4	2	no	—
531	D₈	—	4	2	no	—
532	M₁₆	—	4	2	no	—
533	M₁₆	—	4	2	no	—
534	M₁₆	—	4	1	no	—
535	M₁₆	—	4	1	no	—
536	C₂×C₈	—	2	2	no	—
537	C₂×C₈	—	2	4	no	—
538	C₂×C₈	—	2	4	no	—
539	C₂×C₈	—	4	1	no	—
540	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
541	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
542	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
543	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
544	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	4	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
553	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
554	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	4	no	—
566	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
567	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	2	no	—
571	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
572	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
573	C₄²	C₂⁴×C₁₉	1	2	yes	—
574	C₂³	—	2	4	no	—
575	C₂³	—	8	2	no	—
576	C₂³	—	8	4	no	—
577	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
578	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
579	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
580	Q₈	—	2	4	no	—
581	Q₈	—	2	4	no	—
582	Q₈	—	4	1	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	8	2	no	—
585	D₄	—	2	4	no	—
586	D₄	—	2	4	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	4	no	—
592	D₄	—	8	2	no	—
593	D₄	—	8	4	no	—
594	D₄	—	8	4	no	—
595	D₄	—	8	4	no	—
596	D₄	—	8	4	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	8	4	no	—
608	C₂×C₄	—	8	4	no	—
609	C₂×C₄	—	8	2	no	—
610	C₂×C₄	—	8	4	no	—
611	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
612	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
613	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
614	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
615	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
616	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
617	C₈	—	2	1	no	—
618	C₈	—	2	2	no	—
619	C₈	—	2	2	no	—
620	C₈	—	2	2	no	—
621	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	2	no	—
626	C₂²	—	2	4	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	4	4	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	16	4	no	—
632	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	4	4	no	—
639	C₄	—	4	4	no	—
640	C₄	—	4	4	no	—
641	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
642	C₄	C₁₉×#585	1	1	yes	characteristic
643	C₂	—	4	2	no	—
644	C₂	—	4	1	no	—
645	C₂	—	4	2	no	—
646	C₂	—	8	4	no	—
647	C₂	C₁₉×#3496	1	1	yes	characteristic
648	C₂	C₁₉×#3584	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3551	C₂	semidirect
2. C₁₉×#3337	C₂	semidirect
3. C₁₉×#3327	C₂	semidirect
4. C₁₉×#3322	C₂	semidirect
5. C₁₉×#3282	C₂	semidirect
6. C₁₉×#3256	C₂	semidirect
7. C₁₉×#3203	C₂	semidirect
8. C₁₉×#3202	C₂	semidirect
9. C₁₉×#3199	C₂	semidirect
10. C₁₉×#3168	C₂	semidirect
11. C₁₉×#3060	C₂	semidirect
12. C₁₉×#3057	C₂	semidirect
13. C₁₉×#2931	C₂	semidirect
15. C₂²×SD₁₆×C₁₉	C₂²	semidirect
17. C₂×C₁₉×#131	C₂²	semidirect
22. C₁₉×#552	C₂²	semidirect
25. C₁₉×#546	C₂²	semidirect
28. C₁₉×#537	C₂²	semidirect
32. C₁₉×#529	C₂²	semidirect
33. C₁₉×#499	C₂²	semidirect
35. C₁₉×#488	C₂²	semidirect
36. C₁₉×#485	C₂²	semidirect
37. C₁₉×#484	C₂²	semidirect
39. C₁₉×#480	C₂²	semidirect
40. C₁₉×#479	C₂²	semidirect
41. C₁₉×#478	C₂²	semidirect
42. C₁₉×#470	C₂²	semidirect
43. C₁₉×#470	C₂²	semidirect
47. C₁₉×#468	C₂²	semidirect
48. C₁₉×#467	C₂²	semidirect
51. C₁₉×#465	C₂²	semidirect
52. C₁₉×#465	C₂²	semidirect
53. C₁₉×#464	C₂²	semidirect
55. C₁₉×#452	C₂²	semidirect
56. C₁₉×#451	C₂²	semidirect
59. C₄×Q₁₆×C₁₉	C₂²	semidirect
60. C₄×SD₁₆×C₁₉	C₂²	semidirect
62. C₁₉×#436	C₂²	semidirect
63. C₈×D₄×C₁₉	C₂²	semidirect
64. C₁₉×#427	C₂²	semidirect
65. C₂×C₁₉×#106	C₂²	semidirect
66. C₁₉×#423	C₂²	semidirect
67. C₁₉×#419	C₂²	semidirect
68. C₁₉×#418	C₂²	semidirect
69. C₁₉×#417	C₂²	semidirect
71. C₁₉×#408	C₂²	semidirect
72. C₂×C₄×C₈×C₁₉	C₂²	semidirect
249. #62327	C₁₉	direct (N × H)
298. #3551	C₂×C₁₉	semidirect
299. #3337	C₂×C₁₉	semidirect
300. #3327	C₂×C₁₉	semidirect
301. #3322	C₂×C₁₉	semidirect
302. #3282	C₂×C₁₉	semidirect
303. #3256	C₂×C₁₉	semidirect
304. #3203	C₂×C₁₉	semidirect
305. #3202	C₂×C₁₉	semidirect
306. #3199	C₂×C₁₉	semidirect
307. #3168	C₂×C₁₉	semidirect
308. #3060	C₂×C₁₉	semidirect
309. #3057	C₂×C₁₉	semidirect
310. #2931	C₂×C₁₉	semidirect
333. C₂²×SD₁₆	C₂²×C₁₉	semidirect
335. C₂×#131	C₂²×C₁₉	semidirect
340. #552	C₂²×C₁₉	semidirect
343. #546	C₂²×C₁₉	semidirect
346. #537	C₂²×C₁₉	semidirect
350. #529	C₂²×C₁₉	semidirect
351. #499	C₂²×C₁₉	semidirect
353. #488	C₂²×C₁₉	semidirect
354. #485	C₂²×C₁₉	semidirect
355. #484	C₂²×C₁₉	semidirect
357. #480	C₂²×C₁₉	semidirect
358. #479	C₂²×C₁₉	semidirect
359. #478	C₂²×C₁₉	semidirect
360. #470	C₂²×C₁₉	semidirect
361. #470	C₂²×C₁₉	semidirect
365. #468	C₂²×C₁₉	semidirect
366. #467	C₂²×C₁₉	semidirect
369. #465	C₂²×C₁₉	semidirect
370. #465	C₂²×C₁₉	semidirect
371. #464	C₂²×C₁₉	semidirect
373. #452	C₂²×C₁₉	semidirect
374. #451	C₂²×C₁₉	semidirect
377. C₄×Q₁₆	C₂²×C₁₉	semidirect
378. C₄×SD₁₆	C₂²×C₁₉	semidirect
380. #436	C₂²×C₁₉	semidirect
381. C₈×D₄	C₂²×C₁₉	semidirect
382. #427	C₂²×C₁₉	semidirect
383. C₂×#106	C₂²×C₁₉	semidirect
384. #423	C₂²×C₁₉	semidirect
385. #419	C₂²×C₁₉	semidirect
386. #418	C₂²×C₁₉	semidirect
387. #417	C₂²×C₁₉	semidirect
389. #408	C₂²×C₁₉	semidirect
390. C₂×C₄×C₈	C₂²×C₁₉	semidirect
491. C₁₉	#62327	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×#3551	2
C₁₉×#3337	2
C₁₉×#3327	2
C₁₉×#3322	2
C₁₉×#3282	2
C₁₉×#3256	2
C₁₉×#3203	2
C₁₉×#3202	2
C₁₉×#3199	2
C₁₉×#3168	2
C₁₉×#3060	2
C₁₉×#3057	2
C₁₉×#2931	2
#62327	19

Subgroups — C19×#62327 #18068286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62327 #18068286