Subgroups — C₁₉×#11217 #18017176

Order 4864.

778 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#428	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1736	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
7	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
15	C₁₉×#428	—	2	2	no	—
16	C₁₉×#428	C₄	1	4	yes	complemented
17	C₂×C₁₉×#107	—	2	1	no	—
18	C₂×C₁₉×#106	—	2	1	no	—
19	C₁₉×#389	—	2	1	no	—
20	C₁₉×#389	—	2	1	no	—
21	C₁₉×#385	—	2	2	no	—
22	C₁₉×#384	—	2	1	no	—
23	C₁₉×#382	—	2	1	no	—
24	C₂×C₁₉×#95	—	2	2	no	—
25	C₁₉×#343	—	2	2	no	—
26	C₁₉×#340	—	2	1	no	—
27	C₁₉×#340	—	2	1	no	—
28	C₁₉×#339	—	2	2	no	—
29	C₁₉×#339	—	2	2	no	—
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×C₄×C₁₉	D₄	1	2	yes	—
33	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
44	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
45	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×C₁₉	—	2	1	no	—
48	C₁₉×#117	—	2	1	no	—
49	C₁₉×#117	—	2	1	no	—
50	C₁₉×#117	—	2	1	no	—
51	C₁₉×#117	—	2	1	no	—
52	C₁₉×#117	—	2	1	no	—
53	C₁₉×#117	—	2	1	no	—
54	C₁₉×#117	C₂×C₄	1	2	yes	—
55	C₁₉×#117	D₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	—	2	1	no	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	—	2	1	no	—
79	C₂×C₄²×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	2	1	no	—
81	C₂×C₄²×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	—	2	1	no	—
83	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
84	C₁₉×#107	—	2	4	no	—
85	C₁₉×#106	—	2	4	no	—
86	C₁₉×#95	—	2	2	no	—
87	C₁₉×#95	—	2	2	no	—
88	C₁₉×#95	—	4	4	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	1	no	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	1	no	—
97	C₂²×C₄×C₁₉	—	2	1	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	4	1	no	—
102	C₂²×C₄×C₁₉	—	4	1	no	—
103	C₂²×C₄×C₁₉	—	4	1	no	—
104	C₂²×C₄×C₁₉	—	4	1	no	—
105	C₂²×C₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	4	2	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	1	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
125	M₁₆×C₁₉	—	2	2	no	—
126	M₁₆×C₁₉	—	2	2	no	—
127	M₁₆×C₁₉	—	2	2	no	—
128	M₁₆×C₁₉	—	2	2	no	—
129	M₁₆×C₁₉	—	2	2	no	—
130	M₁₆×C₁₉	—	4	1	no	—
131	M₁₆×C₁₉	—	4	1	no	—
132	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	complemented
133	C₂×C₈×C₁₉	—	2	2	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	—	4	1	no	—
138	C₂×C₈×C₁₉	—	4	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	2	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	8	2	no	—
154	C₄⋊C₄×C₁₉	—	8	2	no	—
155	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
156	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
157	C₂²⋊C₄×C₁₉	—	2	2	no	—
158	C₂²⋊C₄×C₁₉	—	2	2	no	—
159	C₂²⋊C₄×C₁₉	—	4	1	no	—
160	C₂²⋊C₄×C₁₉	—	4	1	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	—	2	2	no	—
164	C₄²×C₁₉	—	2	2	no	—
165	C₄²×C₁₉	—	4	1	no	—
166	C₄²×C₁₉	—	4	1	no	—
167	C₄²×C₁₉	—	4	1	no	—
168	C₄²×C₁₉	—	4	1	no	—
169	#11217	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	2	1	no	—
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
175	C₂³×C₁₉	#120	1	1	yes	characteristic
176	C₂³×C₁₉	#121	1	1	yes	characteristic
177	C₂³×C₁₉	#121	1	1	yes	characteristic
178	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂³×C₁₉	#123	1	1	yes	characteristic
180	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
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	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	4	4	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	1	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	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	8	2	no	—
207	C₂×C₄×C₁₉	—	8	1	no	—
208	C₂×C₄×C₁₉	—	8	1	no	—
209	C₂×C₄×C₁₉	—	8	2	no	—
210	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
217	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
218	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
223	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
226	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
228	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
230	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
232	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
233	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
234	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
235	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
236	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
238	C₈×C₁₉	—	2	4	no	—
239	C₈×C₁₉	—	4	2	no	—
240	C₂×#428	C₂×C₁₉	1	1	yes	characteristic
241	#2317	C₂×C₁₉	1	1	yes	characteristic
242	C₂×#343	C₂×C₁₉	1	1	yes	characteristic
243	#1736	C₂×C₁₉	1	1	yes	characteristic
244	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
245	C₂×#339	C₂×C₁₉	1	1	yes	characteristic
246	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic
247	C₂²×C₁₉	—	2	1	no	—
248	C₂²×C₁₉	—	2	1	no	—
249	C₂²×C₁₉	—	2	1	no	—
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	2	1	no	—
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	#386	1	1	yes	characteristic
260	C₂²×C₁₉	#387	1	1	yes	characteristic
261	C₂²×C₁₉	#389	1	1	yes	characteristic
262	C₂²×C₁₉	#394	1	1	yes	characteristic
263	C₂²×C₁₉	#395	1	1	yes	characteristic
264	C₂²×C₁₉	#396	1	1	yes	characteristic
265	C₂²×C₁₉	#398	1	1	yes	characteristic
266	C₂²×C₁₉	#453	1	1	yes	characteristic
267	C₂²×C₁₉	#454	1	1	yes	characteristic
268	C₂²×C₁₉	#455	1	1	yes	characteristic
269	C₂²×C₁₉	#456	1	1	yes	characteristic
270	C₄×C₁₉	—	4	4	no	—
271	C₄×C₁₉	—	4	2	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	8	2	no	—
274	C₄×C₁₉	—	8	1	no	—
275	C₄×C₁₉	—	8	2	no	—
276	C₄×C₁₉	—	8	1	no	—
277	C₄×C₁₉	#380	1	1	yes	characteristic
278	C₄×C₁₉	#387	1	1	yes	characteristic
279	C₄×C₁₉	#389	1	1	yes	characteristic
280	C₄×C₁₉	#391	1	1	yes	characteristic
281	C₄×C₁₉	#396	1	1	yes	characteristic
282	C₄×C₁₉	#398	1	1	yes	characteristic
283	C₄×C₁₉	#398	1	1	yes	characteristic
284	C₄×C₁₉	#400	1	1	yes	characteristic
285	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
286	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
289	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
290	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
291	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
292	#428	—	2	2	no	—
293	#428	C₄×C₁₉	1	4	yes	complemented
294	C₂×#107	—	2	1	no	—
295	C₂×#106	—	2	1	no	—
296	#389	—	2	1	no	—
297	#389	—	2	1	no	—
298	#385	—	2	2	no	—
299	#384	—	2	1	no	—
300	#382	—	2	1	no	—
301	C₂×#95	—	2	2	no	—
302	#343	—	2	2	no	—
303	#340	—	2	1	no	—
304	#340	—	2	1	no	—
305	#339	—	2	2	no	—
306	#339	—	2	2	no	—
307	C₂×C₁₉	—	2	1	no	—
308	C₂×C₁₉	—	2	1	no	—
309	C₂×C₁₉	—	2	1	no	—
310	C₂×C₁₉	—	2	1	no	—
311	C₂×C₁₉	#1441	1	1	yes	characteristic
312	C₂×C₁₉	#1882	1	1	yes	characteristic
313	C₂×C₁₉	#1883	1	1	yes	characteristic
314	C₂×C₁₉	#2037	1	1	yes	characteristic
315	C₂×C₁₉	#2038	1	1	yes	characteristic
316	C₂×C₁₉	#2060	1	1	yes	characteristic
317	C₂×C₁₉	#2061	1	1	yes	characteristic
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	1	no	—
320	C₂³×C₄	D₄×C₁₉	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
331	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
332	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
333	C₂×M₁₆	Q₈×C₁₉	1	2	yes	—
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	—	2	1	no	—
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	—	2	1	no	—
339	#117	—	2	1	no	—
340	#117	—	2	1	no	—
341	#117	—	2	1	no	—
342	#117	C₂×C₄×C₁₉	1	2	yes	—
343	#117	D₄×C₁₉	1	2	yes	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
358	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
360	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	Q₈×C₁₉	1	2	yes	—
372	#107	—	2	4	no	—
373	#106	—	2	4	no	—
374	#95	—	2	2	no	—
375	#95	—	2	2	no	—
376	#95	—	4	4	no	—
377	C₁₉	#11217	1	1	yes	characteristic, direct product factor, Sylow
378	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	—	4	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
408	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
409	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
414	M₁₆	—	2	2	no	—
415	M₁₆	—	2	2	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	4	1	no	—
420	M₁₆	—	4	1	no	—
421	M₁₆	C₄⋊C₄×C₁₉	1	4	yes	complemented
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	4	1	no	—
427	C₂×C₈	—	4	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	4	1	no	—
437	C₄⋊C₄	—	4	1	no	—
438	C₄⋊C₄	—	4	1	no	—
439	C₄⋊C₄	—	4	1	no	—
440	C₄⋊C₄	—	4	1	no	—
441	C₄⋊C₄	—	4	1	no	—
442	C₄⋊C₄	—	8	2	no	—
443	C₄⋊C₄	—	8	2	no	—
444	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
445	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	4	1	no	—
449	C₂²⋊C₄	—	4	1	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	4	1	no	—
455	C₄²	—	4	1	no	—
456	C₄²	—	4	1	no	—
457	C₄²	—	4	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
463	C₂³	C₁₉×#120	1	1	yes	characteristic
464	C₂³	C₁₉×#121	1	1	yes	characteristic
465	C₂³	C₁₉×#121	1	1	yes	characteristic
466	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
467	C₂³	C₁₉×#123	1	1	yes	characteristic
468	C₂³	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	—	8	1	no	—
497	C₂×C₄	—	8	2	no	—
498	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
499	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
500	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
501	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
502	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₄×Q₈×C₁₉	1	1	yes	characteristic
504	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
505	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
506	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
507	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
508	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
509	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
510	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
511	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
512	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
513	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
514	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
515	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
516	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
517	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
518	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
519	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
520	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
521	C₂×C₄	C₁₉×#125	1	1	yes	characteristic
522	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
523	C₂×C₄	C₁₉×#126	1	1	yes	characteristic
524	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
525	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
526	C₈	—	2	4	no	—
527	C₈	—	4	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	C₁₉×#386	1	1	yes	characteristic
541	C₂²	C₁₉×#387	1	1	yes	characteristic
542	C₂²	C₁₉×#389	1	1	yes	characteristic
543	C₂²	C₁₉×#394	1	1	yes	characteristic
544	C₂²	C₁₉×#395	1	1	yes	characteristic
545	C₂²	C₁₉×#396	1	1	yes	characteristic
546	C₂²	C₁₉×#398	1	1	yes	characteristic
547	C₂²	C₁₉×#453	1	1	yes	characteristic
548	C₂²	C₁₉×#454	1	1	yes	characteristic
549	C₂²	C₁₉×#455	1	1	yes	characteristic
550	C₂²	C₁₉×#456	1	1	yes	characteristic
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	8	2	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	2	no	—
558	C₄	C₁₉×#380	1	1	yes	characteristic
559	C₄	C₁₉×#387	1	1	yes	characteristic
560	C₄	C₁₉×#389	1	1	yes	characteristic
561	C₄	C₁₉×#391	1	1	yes	characteristic
562	C₄	C₁₉×#396	1	1	yes	characteristic
563	C₄	C₁₉×#398	1	1	yes	characteristic
564	C₄	C₁₉×#398	1	1	yes	characteristic
565	C₄	C₁₉×#400	1	1	yes	characteristic
566	C₂	—	2	1	no	—
567	C₂	—	2	1	no	—
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	C₁₉×#1441	1	1	yes	characteristic
571	C₂	C₁₉×#1882	1	1	yes	characteristic
572	C₂	C₁₉×#1883	1	1	yes	characteristic
573	C₂	C₁₉×#2037	1	1	yes	characteristic
574	C₂	C₁₉×#2038	1	1	yes	characteristic
575	C₂	C₁₉×#2060	1	1	yes	characteristic
576	C₂	C₁₉×#2061	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₁₉×#428	C₄	semidirect
132. M₁₆×C₁₉	C₄⋊C₄	semidirect
169. #11217	C₁₉	direct (N × H)
293. #428	C₄×C₁₉	semidirect
377. C₁₉	#11217	direct (N × H)
421. M₁₆	C₄⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#428	2
C₁₉×#2317	2
C₂×C₁₉×#343	2
C₁₉×#1736	2
C₂×C₁₉×#339	2
C₁₉×C₄⋊#95	2
#11217	19

Subgroups — C19×#11217 #18017176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11217 #18017176