Subgroups — C₁₉×#11015 #18016974

Order 4864.

1242 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#137	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#421	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#137	—	2	2	no	—
11	C₂×C₁₉×#137	—	2	2	no	—
12	C₂×C₁₉×#137	—	2	2	no	—
13	C₂×C₁₉×#137	—	2	2	no	—
14	C₂×C₁₉×#137	—	2	2	no	—
15	C₂×C₁₉×#137	—	2	2	no	—
16	C₂²×Q₁₆×C₁₉	C₄	1	2	yes	complemented
17	C₂²×SD₁₆×C₁₉	C₄	1	2	yes	complemented
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₁₉×#421	—	2	2	no	—
24	C₁₉×#421	—	2	2	no	—
25	C₂×C₁₉×#104	—	2	2	no	—
26	C₁₉×#419	—	2	2	no	—
27	C₁₉×#419	—	2	2	no	—
28	C₂×C₁₉×#103	—	2	2	no	—
29	C₂×C₁₉×#101	—	2	2	no	—
30	C₂×C₁₉×#101	—	2	2	no	—
31	C₂×C₁₉×#101	—	2	2	no	—
32	C₁₉×#408	—	2	2	no	—
33	C₁₉×#408	—	2	2	no	—
34	C₁₉×#407	—	2	2	no	—
35	C₁₉×#344	—	2	2	no	—
36	C₁₉×#338	—	2	2	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	1	no	—
43	C₂×#41×C₁₉	—	2	1	no	—
44	C₂×#41×C₁₉	—	2	1	no	—
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂×#41×C₁₉	—	2	1	no	—
47	C₂×#41×C₁₉	D₄	1	2	yes	—
48	C₂×#41×C₁₉	D₄	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	—	2	1	no	—
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	—	2	1	no	—
53	C₂²×Q₈×C₁₉	—	2	1	no	—
54	C₂²×Q₈×C₁₉	—	2	1	no	—
55	C₂²×Q₈×C₁₉	—	2	1	no	—
56	C₂²×Q₈×C₁₉	—	2	1	no	—
57	C₂²×Q₈×C₁₉	—	2	1	no	—
58	C₂²×Q₈×C₁₉	—	2	1	no	—
59	C₂²×Q₈×C₁₉	—	2	1	no	—
60	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
61	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
63	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
64	C₂²×D₄×C₁₉	—	2	1	no	—
65	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₂³×C₄×C₁₉	—	2	1	no	—
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#137	—	2	8	no	—
70	C₁₉×#137	—	2	8	no	—
71	C₁₉×#137	—	2	8	no	—
72	C₁₉×#137	—	2	8	no	—
73	C₂×Q₁₆×C₁₉	—	2	4	no	—
74	C₂×Q₁₆×C₁₉	—	2	4	no	—
75	C₂×Q₁₆×C₁₉	—	2	4	no	—
76	C₂×SD₁₆×C₁₉	—	2	4	no	—
77	C₂×SD₁₆×C₁₉	—	2	4	no	—
78	C₂×SD₁₆×C₁₉	—	2	4	no	—
79	C₂×M₁₆×C₁₉	—	2	1	no	—
80	C₂×M₁₆×C₁₉	—	2	1	no	—
81	C₂×M₁₆×C₁₉	—	2	1	no	—
82	C₂×M₁₆×C₁₉	—	2	1	no	—
83	C₂×M₁₆×C₁₉	—	2	1	no	—
84	C₂×M₁₆×C₁₉	—	2	1	no	—
85	C₂×M₁₆×C₁₉	—	2	1	no	—
86	C₂×M₁₆×C₁₉	—	2	1	no	—
87	C₂×M₁₆×C₁₉	—	2	1	no	—
88	C₂×M₁₆×C₁₉	—	2	1	no	—
89	C₂×M₁₆×C₁₉	—	2	1	no	—
90	C₂×M₁₆×C₁₉	—	2	1	no	—
91	C₂×M₁₆×C₁₉	—	2	1	no	—
92	C₂×M₁₆×C₁₉	—	2	1	no	—
93	C₂×M₁₆×C₁₉	—	2	1	no	—
94	C₂×M₁₆×C₁₉	—	2	1	no	—
95	C₂×M₁₆×C₁₉	—	2	1	no	—
96	C₂×M₁₆×C₁₉	—	2	1	no	—
97	C₂×M₁₆×C₁₉	—	2	1	no	—
98	C₂×M₁₆×C₁₉	—	2	1	no	—
99	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
100	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
101	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
102	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
103	C₂²×C₈×C₁₉	—	2	1	no	—
104	C₂²×C₈×C₁₉	—	2	1	no	—
105	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
106	C₂²×C₈×C₁₉	D₄	1	2	yes	—
107	C₁₉×#117	—	2	1	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₁₉×#117	D₄	1	2	yes	—
111	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	—	2	1	no	—
114	C₁₉×#104	—	2	8	no	—
115	C₁₉×#103	—	2	8	no	—
116	C₁₉×#101	—	2	8	no	—
117	C₁₉×C₂²⋊C₈	—	2	8	no	—
118	C₂⁴×C₁₉	—	2	1	no	—
119	C₂⁴×C₁₉	#41	1	1	yes	characteristic
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	2	2	no	—
127	#41×C₁₉	—	2	2	no	—
128	#41×C₁₉	—	4	1	no	—
129	#41×C₁₉	—	4	1	no	—
130	#41×C₁₉	—	4	1	no	—
131	#41×C₁₉	—	4	1	no	—
132	#41×C₁₉	—	4	1	no	—
133	#41×C₁₉	—	4	1	no	—
134	#41×C₁₉	—	4	1	no	—
135	#41×C₁₉	—	4	1	no	—
136	C₂×Q₈×C₁₉	—	2	2	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	2	2	no	—
141	C₂×Q₈×C₁₉	—	2	2	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	—	2	2	no	—
145	C₂×Q₈×C₁₉	—	2	2	no	—
146	C₂×Q₈×C₁₉	—	2	1	no	—
147	C₂×Q₈×C₁₉	—	2	1	no	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	—	2	2	no	—
150	C₂×Q₈×C₁₉	—	2	2	no	—
151	C₂×Q₈×C₁₉	—	2	2	no	—
152	C₂×Q₈×C₁₉	—	2	2	no	—
153	C₂×Q₈×C₁₉	—	2	2	no	—
154	C₂×Q₈×C₁₉	—	2	2	no	—
155	C₂×Q₈×C₁₉	—	2	2	no	—
156	C₂×Q₈×C₁₉	—	4	1	no	—
157	C₂×Q₈×C₁₉	—	4	1	no	—
158	C₂×Q₈×C₁₉	—	4	1	no	—
159	C₂×Q₈×C₁₉	—	4	1	no	—
160	C₂×Q₈×C₁₉	—	4	1	no	—
161	C₂×Q₈×C₁₉	—	4	1	no	—
162	C₂×Q₈×C₁₉	—	4	1	no	—
163	C₂×Q₈×C₁₉	—	4	1	no	—
164	C₂×Q₈×C₁₉	—	4	1	no	—
165	C₂×Q₈×C₁₉	—	4	1	no	—
166	C₂×Q₈×C₁₉	—	4	1	no	—
167	C₂×Q₈×C₁₉	—	4	1	no	—
168	C₂×Q₈×C₁₉	C₂²⋊C₄	1	4	yes	—
169	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
170	C₂×D₄×C₁₉	—	2	2	no	—
171	C₂×D₄×C₁₉	—	2	2	no	—
172	C₂×D₄×C₁₉	—	2	1	no	—
173	C₂×D₄×C₁₉	—	2	1	no	—
174	C₂×D₄×C₁₉	—	2	1	no	—
175	C₂×D₄×C₁₉	—	2	1	no	—
176	C₂×D₄×C₁₉	—	2	1	no	—
177	C₂×D₄×C₁₉	—	4	1	no	—
178	C₂×D₄×C₁₉	—	4	1	no	—
179	C₂×D₄×C₁₉	—	4	1	no	—
180	C₂×D₄×C₁₉	—	4	1	no	—
181	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	2	2	no	—
186	C₂²×C₄×C₁₉	—	2	2	no	—
187	C₂²×C₄×C₁₉	—	2	2	no	—
188	C₂²×C₄×C₁₉	—	4	1	no	—
189	C₂²×C₄×C₁₉	—	4	1	no	—
190	C₂²×C₄×C₁₉	—	4	1	no	—
191	C₂²×C₄×C₁₉	—	4	1	no	—
192	C₂²×C₄×C₁₉	—	4	1	no	—
193	C₂²×C₄×C₁₉	—	4	1	no	—
194	C₂²×C₄×C₁₉	—	4	1	no	—
195	C₂²×C₄×C₁₉	—	4	1	no	—
196	C₂²×C₄×C₁₉	—	4	1	no	—
197	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
209	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
210	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
211	Q₁₆×C₁₉	—	2	16	no	—
212	SD₁₆×C₁₉	—	2	16	no	—
213	M₁₆×C₁₉	—	2	2	no	—
214	M₁₆×C₁₉	—	2	2	no	—
215	M₁₆×C₁₉	—	2	2	no	—
216	M₁₆×C₁₉	—	2	2	no	—
217	M₁₆×C₁₉	—	2	2	no	—
218	M₁₆×C₁₉	—	2	2	no	—
219	M₁₆×C₁₉	—	2	2	no	—
220	M₁₆×C₁₉	—	2	2	no	—
221	M₁₆×C₁₉	—	4	1	no	—
222	M₁₆×C₁₉	—	4	1	no	—
223	M₁₆×C₁₉	—	4	1	no	—
224	M₁₆×C₁₉	—	4	1	no	—
225	M₁₆×C₁₉	—	4	1	no	—
226	M₁₆×C₁₉	—	4	1	no	—
227	M₁₆×C₁₉	—	4	1	no	—
228	M₁₆×C₁₉	—	4	1	no	—
229	C₂×C₈×C₁₉	—	2	2	no	—
230	C₂×C₈×C₁₉	—	2	2	no	—
231	C₂×C₈×C₁₉	—	2	2	no	—
232	C₂×C₈×C₁₉	—	2	2	no	—
233	C₂×C₈×C₁₉	—	2	2	no	—
234	C₂×C₈×C₁₉	—	2	2	no	—
235	C₂×C₈×C₁₉	—	2	2	no	—
236	C₂×C₈×C₁₉	—	4	1	no	—
237	C₂×C₈×C₁₉	—	4	1	no	—
238	C₂×C₈×C₁₉	—	4	1	no	—
239	C₂×C₈×C₁₉	—	4	1	no	—
240	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
241	C₄⋊C₄×C₁₉	—	2	2	no	—
242	C₄⋊C₄×C₁₉	—	4	1	no	—
243	C₂²⋊C₄×C₁₉	—	2	2	no	—
244	C₂²⋊C₄×C₁₉	—	4	1	no	—
245	C₄²×C₁₉	—	2	2	no	—
246	C₄²×C₁₉	—	4	1	no	—
247	#11015	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂³×C₁₉	—	2	2	no	—
249	C₂³×C₁₉	—	4	2	no	—
250	C₂³×C₁₉	—	4	1	no	—
251	C₂³×C₁₉	—	4	1	no	—
252	C₂³×C₁₉	—	8	2	no	—
253	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
254	C₂³×C₁₉	#121	1	1	yes	characteristic
255	C₂³×C₁₉	#121	1	1	yes	characteristic
256	C₂³×C₁₉	#121	1	1	yes	characteristic
257	C₂³×C₁₉	#123	1	1	yes	characteristic
258	C₂³×C₁₉	#123	1	1	yes	characteristic
259	C₂³×C₁₉	#124	1	1	yes	characteristic
260	Q₈×C₁₉	—	2	4	no	—
261	Q₈×C₁₉	—	2	2	no	—
262	Q₈×C₁₉	—	2	4	no	—
263	Q₈×C₁₉	—	2	2	no	—
264	Q₈×C₁₉	—	4	2	no	—
265	Q₈×C₁₉	—	4	1	no	—
266	Q₈×C₁₉	—	4	2	no	—
267	Q₈×C₁₉	—	4	1	no	—
268	Q₈×C₁₉	—	4	2	no	—
269	Q₈×C₁₉	—	4	2	no	—
270	Q₈×C₁₉	—	4	2	no	—
271	Q₈×C₁₉	—	4	2	no	—
272	D₄×C₁₉	—	2	2	no	—
273	D₄×C₁₉	—	2	2	no	—
274	D₄×C₁₉	—	4	2	no	—
275	D₄×C₁₉	—	4	2	no	—
276	D₄×C₁₉	—	4	2	no	—
277	D₄×C₁₉	—	4	2	no	—
278	D₄×C₁₉	—	4	1	no	—
279	D₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	2	4	no	—
281	C₂×C₄×C₁₉	—	2	2	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	2	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	2	no	—
286	C₂×C₄×C₁₉	—	4	2	no	—
287	C₂×C₄×C₁₉	—	4	2	no	—
288	C₂×C₄×C₁₉	—	4	2	no	—
289	C₂×C₄×C₁₉	—	4	2	no	—
290	C₂×C₄×C₁₉	—	4	2	no	—
291	C₂×C₄×C₁₉	—	4	2	no	—
292	C₂×C₄×C₁₉	—	4	2	no	—
293	C₂×C₄×C₁₉	—	4	2	no	—
294	C₂×C₄×C₁₉	—	4	2	no	—
295	C₂×C₄×C₁₉	—	8	2	no	—
296	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
300	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
302	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
303	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
304	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
305	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
306	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
307	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
308	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
309	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
310	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
311	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
312	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
313	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
314	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
315	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
316	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
317	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
318	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
319	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
320	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
321	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
322	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
323	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
324	C₈×C₁₉	—	2	4	no	—
325	C₈×C₁₉	—	4	2	no	—
326	C₈×C₁₉	—	4	2	no	—
327	C₈×C₁₉	—	4	2	no	—
328	C₂²×#137	C₂×C₁₉	1	1	yes	characteristic
329	C₂×#421	C₂×C₁₉	1	1	yes	characteristic
330	C₂×#419	C₂×C₁₉	1	1	yes	characteristic, complemented
331	C₂²×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
332	#2879	C₂×C₁₉	1	1	yes	characteristic
333	C₂×#344	C₂×C₁₉	1	1	yes	characteristic, complemented
334	C₂×#338	C₂×C₁₉	1	1	yes	characteristic, complemented
335	C₂²×C₁₉	—	2	2	no	—
336	C₂²×C₁₉	—	2	2	no	—
337	C₂²×C₁₉	—	2	2	no	—
338	C₂²×C₁₉	—	4	1	no	—
339	C₂²×C₁₉	—	4	1	no	—
340	C₂²×C₁₉	—	4	1	no	—
341	C₂²×C₁₉	—	4	1	no	—
342	C₂²×C₁₉	—	4	4	no	—
343	C₂²×C₁₉	—	4	2	no	—
344	C₂²×C₁₉	—	8	2	no	—
345	C₂²×C₁₉	—	8	2	no	—
346	C₂²×C₁₉	#386	1	1	yes	characteristic
347	C₂²×C₁₉	#386	1	1	yes	characteristic
348	C₂²×C₁₉	#390	1	1	yes	characteristic
349	C₂²×C₁₉	#392	1	1	yes	characteristic
350	C₂²×C₁₉	#394	1	1	yes	characteristic
351	C₂²×C₁₉	#394	1	1	yes	characteristic
352	C₂²×C₁₉	#394	1	1	yes	characteristic
353	C₄×C₁₉	—	4	2	no	—
354	C₄×C₁₉	—	4	4	no	—
355	C₄×C₁₉	—	8	2	no	—
356	C₄×C₁₉	#379	1	1	yes	characteristic
357	C₄×C₁₉	#386	1	1	yes	characteristic
358	C₄×C₁₉	#386	1	1	yes	characteristic
359	C₄×C₁₉	#390	1	1	yes	characteristic
360	C₄×C₁₉	#392	1	1	yes	characteristic
361	C₄×C₁₉	#392	1	1	yes	characteristic
362	C₄×C₁₉	#392	1	1	yes	characteristic
363	C₄×C₁₉	#394	1	1	yes	characteristic
364	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
365	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#137	—	2	2	no	—
367	C₂×#137	—	2	2	no	—
368	C₂×#137	—	2	2	no	—
369	C₂×#137	—	2	2	no	—
370	C₂×#137	—	2	2	no	—
371	C₂×#137	—	2	2	no	—
372	C₂²×Q₁₆	C₄×C₁₉	1	2	yes	complemented
373	C₂²×SD₁₆	C₄×C₁₉	1	2	yes	complemented
374	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
375	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
376	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
377	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
379	#421	—	2	2	no	—
380	#421	—	2	2	no	—
381	C₂×#104	—	2	2	no	—
382	#419	—	2	2	no	—
383	#419	—	2	2	no	—
384	C₂×#103	—	2	2	no	—
385	C₂×#101	—	2	2	no	—
386	C₂×#101	—	2	2	no	—
387	C₂×#101	—	2	2	no	—
388	#408	—	2	2	no	—
389	#408	—	2	2	no	—
390	#407	—	2	2	no	—
391	#344	—	2	2	no	—
392	#338	—	2	2	no	—
393	C₂×C₁₉	—	2	1	no	—
394	C₂×C₁₉	—	2	1	no	—
395	C₂×C₁₉	—	2	1	no	—
396	C₂×C₁₉	—	2	1	no	—
397	C₂×C₁₉	—	2	1	no	—
398	C₂×C₁₉	—	2	1	no	—
399	C₂×C₁₉	—	8	2	no	—
400	C₂×C₁₉	#1438	1	1	yes	characteristic
401	C₂×C₁₉	#1902	1	2	yes	—
402	C₂×#41	—	2	1	no	—
403	C₂×#41	—	2	1	no	—
404	C₂×#41	—	2	1	no	—
405	C₂×#41	—	2	1	no	—
406	C₂×#41	—	2	1	no	—
407	C₂×#41	—	2	1	no	—
408	C₂×#41	—	2	1	no	—
409	C₂×#41	—	2	1	no	—
410	C₂×#41	—	2	1	no	—
411	C₂×#41	—	2	1	no	—
412	C₂×#41	D₄×C₁₉	1	2	yes	—
413	C₂×#41	D₄×C₁₉	1	2	yes	—
414	C₂²×Q₈	—	2	1	no	—
415	C₂²×Q₈	—	2	1	no	—
416	C₂²×Q₈	—	2	1	no	—
417	C₂²×Q₈	—	2	1	no	—
418	C₂²×Q₈	—	2	1	no	—
419	C₂²×Q₈	—	2	1	no	—
420	C₂²×Q₈	—	2	1	no	—
421	C₂²×Q₈	—	2	1	no	—
422	C₂²×Q₈	—	2	1	no	—
423	C₂²×Q₈	—	2	1	no	—
424	C₂²×Q₈	—	2	1	no	—
425	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
426	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
427	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
428	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
431	C₂³×C₄	—	2	1	no	—
432	C₂³×C₄	—	2	1	no	—
433	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
434	#137	—	2	8	no	—
435	#137	—	2	8	no	—
436	#137	—	2	8	no	—
437	#137	—	2	8	no	—
438	C₂×Q₁₆	—	2	4	no	—
439	C₂×Q₁₆	—	2	4	no	—
440	C₂×Q₁₆	—	2	4	no	—
441	C₂×SD₁₆	—	2	4	no	—
442	C₂×SD₁₆	—	2	4	no	—
443	C₂×SD₁₆	—	2	4	no	—
444	C₂×M₁₆	—	2	1	no	—
445	C₂×M₁₆	—	2	1	no	—
446	C₂×M₁₆	—	2	1	no	—
447	C₂×M₁₆	—	2	1	no	—
448	C₂×M₁₆	—	2	1	no	—
449	C₂×M₁₆	—	2	1	no	—
450	C₂×M₁₆	—	2	1	no	—
451	C₂×M₁₆	—	2	1	no	—
452	C₂×M₁₆	—	2	1	no	—
453	C₂×M₁₆	—	2	1	no	—
454	C₂×M₁₆	—	2	1	no	—
455	C₂×M₁₆	—	2	1	no	—
456	C₂×M₁₆	—	2	1	no	—
457	C₂×M₁₆	—	2	1	no	—
458	C₂×M₁₆	—	2	1	no	—
459	C₂×M₁₆	—	2	1	no	—
460	C₂×M₁₆	—	2	1	no	—
461	C₂×M₁₆	—	2	1	no	—
462	C₂×M₁₆	—	2	1	no	—
463	C₂×M₁₆	—	2	1	no	—
464	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
465	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
466	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
467	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
468	C₂²×C₈	—	2	1	no	—
469	C₂²×C₈	—	2	1	no	—
470	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
471	C₂²×C₈	D₄×C₁₉	1	2	yes	—
472	#117	—	2	1	no	—
473	#117	—	2	1	no	—
474	#117	—	2	1	no	—
475	#117	D₄×C₁₉	1	2	yes	—
476	C₂×C₄⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₄²	—	2	1	no	—
479	#104	—	2	8	no	—
480	#103	—	2	8	no	—
481	#101	—	2	8	no	—
482	C₂²⋊C₈	—	2	8	no	—
483	C₁₉	#11015	1	1	yes	characteristic, direct product factor, Sylow
484	C₂⁴	—	2	1	no	—
485	C₂⁴	#41×C₁₉	1	1	yes	characteristic
486	#41	—	2	2	no	—
487	#41	—	2	2	no	—
488	#41	—	2	2	no	—
489	#41	—	2	2	no	—
490	#41	—	2	2	no	—
491	#41	—	2	2	no	—
492	#41	—	2	2	no	—
493	#41	—	2	2	no	—
494	#41	—	4	1	no	—
495	#41	—	4	1	no	—
496	#41	—	4	1	no	—
497	#41	—	4	1	no	—
498	#41	—	4	1	no	—
499	#41	—	4	1	no	—
500	#41	—	4	1	no	—
501	#41	—	4	1	no	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	2	no	—
505	C₂×Q₈	—	2	2	no	—
506	C₂×Q₈	—	2	2	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	2	2	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	2	no	—
515	C₂×Q₈	—	2	2	no	—
516	C₂×Q₈	—	2	2	no	—
517	C₂×Q₈	—	2	2	no	—
518	C₂×Q₈	—	2	2	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	2	no	—
522	C₂×Q₈	—	4	1	no	—
523	C₂×Q₈	—	4	1	no	—
524	C₂×Q₈	—	4	1	no	—
525	C₂×Q₈	—	4	1	no	—
526	C₂×Q₈	—	4	1	no	—
527	C₂×Q₈	—	4	1	no	—
528	C₂×Q₈	—	4	1	no	—
529	C₂×Q₈	—	4	1	no	—
530	C₂×Q₈	—	4	1	no	—
531	C₂×Q₈	—	4	1	no	—
532	C₂×Q₈	—	4	1	no	—
533	C₂×Q₈	—	4	1	no	—
534	C₂×Q₈	C₂²⋊C₄×C₁₉	1	4	yes	—
535	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	4	1	no	—
544	C₂×D₄	—	4	1	no	—
545	C₂×D₄	—	4	1	no	—
546	C₂×D₄	—	4	1	no	—
547	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	4	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	1	no	—
559	C₂²×C₄	—	4	1	no	—
560	C₂²×C₄	—	4	1	no	—
561	C₂²×C₄	—	4	1	no	—
562	C₂²×C₄	—	4	1	no	—
563	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
564	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
565	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
566	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
567	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
574	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
575	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
576	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
577	Q₁₆	—	2	16	no	—
578	SD₁₆	—	2	16	no	—
579	M₁₆	—	2	2	no	—
580	M₁₆	—	2	2	no	—
581	M₁₆	—	2	2	no	—
582	M₁₆	—	2	2	no	—
583	M₁₆	—	2	2	no	—
584	M₁₆	—	2	2	no	—
585	M₁₆	—	2	2	no	—
586	M₁₆	—	2	2	no	—
587	M₁₆	—	4	1	no	—
588	M₁₆	—	4	1	no	—
589	M₁₆	—	4	1	no	—
590	M₁₆	—	4	1	no	—
591	M₁₆	—	4	1	no	—
592	M₁₆	—	4	1	no	—
593	M₁₆	—	4	1	no	—
594	M₁₆	—	4	1	no	—
595	C₂×C₈	—	2	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	2	no	—
598	C₂×C₈	—	2	2	no	—
599	C₂×C₈	—	2	2	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	2	2	no	—
602	C₂×C₈	—	4	1	no	—
603	C₂×C₈	—	4	1	no	—
604	C₂×C₈	—	4	1	no	—
605	C₂×C₈	—	4	1	no	—
606	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	4	1	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	4	1	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	4	2	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	8	2	no	—
618	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
619	C₂³	C₁₉×#121	1	1	yes	characteristic
620	C₂³	C₁₉×#121	1	1	yes	characteristic
621	C₂³	C₁₉×#121	1	1	yes	characteristic
622	C₂³	C₁₉×#123	1	1	yes	characteristic
623	C₂³	C₁₉×#123	1	1	yes	characteristic
624	C₂³	C₁₉×#124	1	1	yes	characteristic
625	Q₈	—	2	4	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	2	4	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	4	2	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	2	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	2	no	—
634	Q₈	—	4	2	no	—
635	Q₈	—	4	2	no	—
636	Q₈	—	4	2	no	—
637	D₄	—	2	2	no	—
638	D₄	—	2	2	no	—
639	D₄	—	4	2	no	—
640	D₄	—	4	2	no	—
641	D₄	—	4	2	no	—
642	D₄	—	4	2	no	—
643	D₄	—	4	1	no	—
644	D₄	—	4	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	2	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	—	4	2	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	8	2	no	—
661	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
662	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
663	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
664	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
665	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
666	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
667	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
668	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
669	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
670	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
671	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
672	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
673	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
674	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
675	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
676	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
677	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
678	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
679	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
680	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
681	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
682	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
683	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
684	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
685	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
686	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
687	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
688	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
689	C₈	—	2	4	no	—
690	C₈	—	4	2	no	—
691	C₈	—	4	2	no	—
692	C₈	—	4	2	no	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	8	2	no	—
703	C₂²	—	8	2	no	—
704	C₂²	C₁₉×#386	1	1	yes	characteristic
705	C₂²	C₁₉×#386	1	1	yes	characteristic
706	C₂²	C₁₉×#390	1	1	yes	characteristic
707	C₂²	C₁₉×#392	1	1	yes	characteristic
708	C₂²	C₁₉×#394	1	1	yes	characteristic
709	C₂²	C₁₉×#394	1	1	yes	characteristic
710	C₂²	C₁₉×#394	1	1	yes	characteristic
711	C₄	—	4	2	no	—
712	C₄	—	4	4	no	—
713	C₄	—	8	2	no	—
714	C₄	C₁₉×#379	1	1	yes	characteristic
715	C₄	C₁₉×#386	1	1	yes	characteristic
716	C₄	C₁₉×#386	1	1	yes	characteristic
717	C₄	C₁₉×#390	1	1	yes	characteristic
718	C₄	C₁₉×#392	1	1	yes	characteristic
719	C₄	C₁₉×#392	1	1	yes	characteristic
720	C₄	C₁₉×#392	1	1	yes	characteristic
721	C₄	C₁₉×#394	1	1	yes	characteristic
722	C₂	—	2	1	no	—
723	C₂	—	2	1	no	—
724	C₂	—	2	1	no	—
725	C₂	—	2	1	no	—
726	C₂	—	2	1	no	—
727	C₂	—	2	1	no	—
728	C₂	—	8	2	no	—
729	C₂	C₁₉×#1438	1	1	yes	characteristic
730	C₂	C₁₉×#1902	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#419	C₂	semidirect
4. C₂²×C₁₉×#101	C₂	semidirect
6. C₂×C₁₉×#344	C₂	semidirect
7. C₂×C₁₉×#338	C₂	semidirect
16. C₂²×Q₁₆×C₁₉	C₄	semidirect
17. C₂²×SD₁₆×C₁₉	C₄	semidirect
247. #11015	C₁₉	direct (N × H)
330. C₂×#419	C₂×C₁₉	semidirect
331. C₂²×#101	C₂×C₁₉	semidirect
333. C₂×#344	C₂×C₁₉	semidirect
334. C₂×#338	C₂×C₁₉	semidirect
372. C₂²×Q₁₆	C₄×C₁₉	semidirect
373. C₂²×SD₁₆	C₄×C₁₉	semidirect
483. C₁₉	#11015	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#137	2
C₂×C₁₉×#421	2
C₂×C₁₉×#419	2
C₂²×C₁₉×#101	2
C₁₉×#2879	2
C₂×C₁₉×#344	2
C₂×C₁₉×#338	2
#11015	19

Subgroups — C19×#11015 #18016974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11015 #18016974