Subgroups — C₁₉×#34878 #18040837

Order 4864.

1794 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2612	C₂	1	4	yes	maximal, complemented
2	C₁₉×#2606	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2605	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2569	C₂	1	2	yes	maximal
5	C₁₉×#2549	C₂	1	2	yes	maximal
6	C₁₉×#2438	C₂	1	4	yes	maximal
7	C₁₉×#2402	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2399	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₉×C₂²⋊Q₈	C₂	1	4	yes	maximal
10	C₁₉×#2295	C₂	1	4	yes	maximal, complemented
11	C₁₉×#2283	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₉×#117	C₂	1	1	yes	maximal, characteristic
13	C₂×C₁₉×#376	C₂	1	1	yes	maximal, characteristic
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
16	C₂×C₁₉×#117	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#400	C₂²	1	4	yes	—
20	C₁₉×#400	C₂²	1	4	yes	—
21	C₁₉×#398	C₂²	1	4	yes	—
22	C₁₉×#398	C₂²	1	4	yes	—
23	C₁₉×#398	C₂²	1	4	yes	—
24	C₁₉×#398	C₂²	1	4	yes	—
25	C₁₉×#395	C₂²	1	4	yes	—
26	C₁₉×#395	C₂²	1	4	yes	—
27	C₁₉×#391	C₂²	1	4	yes	—
28	C₁₉×#391	C₂²	1	4	yes	—
29	C₁₉×#391	C₂²	1	4	yes	—
30	C₁₉×#389	C₂²	1	4	yes	—
31	C₁₉×#389	C₂²	1	4	yes	—
32	C₁₉×#389	C₂²	1	4	yes	—
33	C₁₉×#387	C₂²	1	4	yes	—
34	C₁₉×#387	C₂²	1	4	yes	—
35	C₁₉×#387	C₂²	1	4	yes	—
36	C₁₉×#387	C₂²	1	4	yes	—
37	C₁₉×#387	C₂²	1	4	yes	—
38	C₁₉×#387	C₂²	1	4	yes	—
39	C₁₉×#385	C₂²	1	4	yes	—
40	C₁₉×#385	C₂²	1	4	yes	—
41	C₁₉×#383	C₂²	1	1	yes	characteristic
42	C₁₉×#383	C₂²	1	1	yes	characteristic
43	C₁₉×#382	C₂²	1	2	yes	—
44	C₁₉×#381	C₂²	1	2	yes	—
45	C₁₉×#380	C₂²	1	4	yes	—
46	C₁₉×#380	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
52	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
55	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
57	C₁₉×#376	C₂²	1	1	yes	characteristic
58	C₁₉×#376	C₂²	1	1	yes	characteristic
59	C₁₉×#376	C₂²	1	2	yes	—
60	C₁₉×#376	C₂²	1	2	yes	—
61	C₁₉×#376	C₂²	1	2	yes	—
62	C₁₉×#376	C₂²	1	2	yes	—
63	C₁₉×#376	C₂²	1	2	yes	—
64	C₂×C₁₉×#95	C₂²	1	2	yes	—
65	C₂×C₁₉×#95	C₂²	1	2	yes	—
66	C₄³×C₁₉	C₂²	1	2	yes	—
67	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₁₉×C₂²⋊Q₈	—	2	16	no	—
73	C₄×Q₈×C₁₉	—	2	16	no	—
74	C₁₉×#117	—	2	8	no	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₁₉	—	2	8	no	—
90	C₂×C₄²×C₁₉	Q₈	1	8	yes	complemented
91	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
94	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
98	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
103	C₁₉×#95	C₂³	1	4	yes	—
104	C₁₉×#95	C₂³	1	4	yes	—
105	C₁₉×#95	C₂³	1	2	yes	—
106	C₁₉×#95	C₂³	1	2	yes	—
107	C₁₉×#95	C₂³	1	2	yes	—
108	C₁₉×#95	C₂³	1	2	yes	—
109	C₁₉×#95	C₂³	1	4	yes	—
110	C₁₉×#95	C₂³	1	2	yes	—
111	C₁₉×#95	C₂³	1	2	yes	—
112	C₁₉×#95	C₂³	1	2	yes	—
113	C₁₉×#95	C₂³	1	2	yes	—
114	C₁₉×#95	C₂³	1	4	yes	—
115	C₁₉×#95	C₂³	1	2	yes	—
116	C₁₉×#95	C₂³	1	2	yes	—
117	C₁₉×#95	C₂³	1	4	yes	—
118	C₁₉×#95	C₂³	1	4	yes	—
119	C₁₉×#95	C₂³	1	2	yes	—
120	C₁₉×#95	C₂³	1	2	yes	—
121	C₁₉×#95	C₂³	1	4	yes	—
122	C₁₉×#95	C₂³	1	4	yes	—
123	C₁₉×#95	C₂³	1	4	yes	—
124	C₁₉×#95	C₂³	1	4	yes	—
125	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
126	C₂×Q₈×C₁₉	—	2	8	no	—
127	C₂×Q₈×C₁₉	—	2	8	no	—
128	C₂×Q₈×C₁₉	—	4	4	no	—
129	C₂²×C₄×C₁₉	—	2	4	no	—
130	C₂²×C₄×C₁₉	—	2	4	no	—
131	C₂²×C₄×C₁₉	—	2	8	no	—
132	C₂²×C₄×C₁₉	—	2	8	no	—
133	C₂²×C₄×C₁₉	—	4	2	no	—
134	C₂²×C₄×C₁₉	—	4	4	no	—
135	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
136	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
137	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
150	C₄⋊C₄×C₁₉	—	2	8	no	—
151	C₄⋊C₄×C₁₉	—	2	8	no	—
152	C₄⋊C₄×C₁₉	—	2	8	no	—
153	C₄⋊C₄×C₁₉	—	2	8	no	—
154	C₄⋊C₄×C₁₉	—	2	8	no	—
155	C₄⋊C₄×C₁₉	—	2	8	no	—
156	C₄⋊C₄×C₁₉	—	2	8	no	—
157	C₄⋊C₄×C₁₉	—	4	4	no	—
158	C₄⋊C₄×C₁₉	—	4	4	no	—
159	C₄⋊C₄×C₁₉	—	4	4	no	—
160	C₄⋊C₄×C₁₉	—	4	4	no	—
161	C₂²⋊C₄×C₁₉	—	2	4	no	—
162	C₂²⋊C₄×C₁₉	—	2	8	no	—
163	C₂²⋊C₄×C₁₉	#41	1	8	yes	—
164	C₄²×C₁₉	—	2	8	no	—
165	C₄²×C₁₉	—	2	4	no	—
166	C₄²×C₁₉	—	2	8	no	—
167	C₄²×C₁₉	—	2	8	no	—
168	C₄²×C₁₉	—	2	8	no	—
169	C₄²×C₁₉	—	4	2	no	—
170	C₄²×C₁₉	—	4	2	no	—
171	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
172	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
173	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
174	C₄²×C₁₉	C₂×Q₈	1	4	yes	—
175	C₄²×C₁₉	#41	1	8	yes	—
176	#34878	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	2	2	no	—
179	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
180	C₂³×C₁₉	C₂×#41	1	4	yes	—
181	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
182	Q₈×C₁₉	—	4	16	no	—
183	C₂×C₄×C₁₉	—	2	8	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	4	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	8	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	16	no	—
208	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
209	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
210	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
211	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
212	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
213	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
214	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
215	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
216	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
217	#2612	C₂×C₁₉	1	4	yes	complemented
218	#2606	C₂×C₁₉	1	2	yes	complemented
219	#2605	C₂×C₁₉	1	2	yes	complemented
220	#2569	C₂×C₁₉	1	2	yes	—
221	#2549	C₂×C₁₉	1	2	yes	—
222	#2438	C₂×C₁₉	1	4	yes	—
223	#2402	C₂×C₁₉	1	2	yes	complemented
224	#2399	C₂×C₁₉	1	2	yes	complemented
225	C₄×C₂²⋊Q₈	C₂×C₁₉	1	4	yes	—
226	#2295	C₂×C₁₉	1	4	yes	complemented
227	#2283	C₂×C₁₉	1	1	yes	characteristic
228	C₄×#117	C₂×C₁₉	1	1	yes	characteristic
229	C₂×#376	C₂×C₁₉	1	1	yes	characteristic
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	2	8	no	—
233	C₂²×C₁₉	#533	1	4	yes	—
234	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
235	C₂²×C₁₉	C₂²×#41	1	2	yes	—
236	C₂²×C₁₉	C₂²×#41	1	2	yes	—
237	C₂²×C₁₉	#585	1	2	yes	—
238	C₄×C₁₉	—	2	2	no	—
239	C₄×C₁₉	—	2	2	no	—
240	C₄×C₁₉	—	2	2	no	—
241	C₄×C₁₉	—	2	2	no	—
242	C₄×C₁₉	—	2	2	no	—
243	C₄×C₁₉	—	2	8	no	—
244	C₄×C₁₉	—	2	8	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	—	4	4	no	—
247	C₄×C₁₉	—	4	4	no	—
248	C₄×C₁₉	—	4	4	no	—
249	C₄×C₁₉	#533	1	4	yes	—
250	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
251	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
252	C₂×#117	C₂²×C₁₉	1	2	yes	—
253	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
254	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
255	#400	C₂²×C₁₉	1	4	yes	—
256	#400	C₂²×C₁₉	1	4	yes	—
257	#398	C₂²×C₁₉	1	4	yes	—
258	#398	C₂²×C₁₉	1	4	yes	—
259	#398	C₂²×C₁₉	1	4	yes	—
260	#398	C₂²×C₁₉	1	4	yes	—
261	#395	C₂²×C₁₉	1	4	yes	—
262	#395	C₂²×C₁₉	1	4	yes	—
263	#391	C₂²×C₁₉	1	4	yes	—
264	#391	C₂²×C₁₉	1	4	yes	—
265	#391	C₂²×C₁₉	1	4	yes	—
266	#389	C₂²×C₁₉	1	4	yes	—
267	#389	C₂²×C₁₉	1	4	yes	—
268	#389	C₂²×C₁₉	1	4	yes	—
269	#387	C₂²×C₁₉	1	4	yes	—
270	#387	C₂²×C₁₉	1	4	yes	—
271	#387	C₂²×C₁₉	1	4	yes	—
272	#387	C₂²×C₁₉	1	4	yes	—
273	#387	C₂²×C₁₉	1	4	yes	—
274	#387	C₂²×C₁₉	1	4	yes	—
275	#385	C₂²×C₁₉	1	4	yes	—
276	#385	C₂²×C₁₉	1	4	yes	—
277	#383	C₂²×C₁₉	1	1	yes	characteristic
278	#383	C₂²×C₁₉	1	1	yes	characteristic
279	#382	C₂²×C₁₉	1	2	yes	—
280	#381	C₂²×C₁₉	1	2	yes	—
281	#380	C₂²×C₁₉	1	4	yes	—
282	#380	C₂²×C₁₉	1	2	yes	—
283	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
284	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
285	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
286	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
287	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
288	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
289	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
290	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
292	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
293	#376	C₂²×C₁₉	1	2	yes	—
294	#376	C₂²×C₁₉	1	2	yes	—
295	#376	C₂²×C₁₉	1	2	yes	—
296	#376	C₂²×C₁₉	1	1	yes	characteristic
297	#376	C₂²×C₁₉	1	1	yes	characteristic
298	#376	C₂²×C₁₉	1	2	yes	—
299	#376	C₂²×C₁₉	1	2	yes	—
300	C₂×#95	C₂²×C₁₉	1	2	yes	—
301	C₂×#95	C₂²×C₁₉	1	2	yes	—
302	C₄³	C₂²×C₁₉	1	2	yes	—
303	C₂×C₁₉	—	2	4	no	—
304	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
305	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
306	C₂×C₁₉	#3458	1	1	yes	characteristic
307	C₂×C₁₉	#3475	1	4	yes	—
308	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
309	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
310	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
313	C₂²⋊Q₈	—	2	16	no	—
314	C₄×Q₈	—	2	16	no	—
315	#117	—	2	8	no	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
321	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
328	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
329	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
330	C₂×C₄²	—	2	8	no	—
331	C₂×C₄²	Q₈×C₁₉	1	8	yes	complemented
332	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
333	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
334	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
335	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
336	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
337	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
338	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
339	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
344	#95	C₂³×C₁₉	1	4	yes	—
345	#95	C₂³×C₁₉	1	4	yes	—
346	#95	C₂³×C₁₉	1	2	yes	—
347	#95	C₂³×C₁₉	1	2	yes	—
348	#95	C₂³×C₁₉	1	2	yes	—
349	#95	C₂³×C₁₉	1	2	yes	—
350	#95	C₂³×C₁₉	1	4	yes	—
351	#95	C₂³×C₁₉	1	2	yes	—
352	#95	C₂³×C₁₉	1	2	yes	—
353	#95	C₂³×C₁₉	1	2	yes	—
354	#95	C₂³×C₁₉	1	2	yes	—
355	#95	C₂³×C₁₉	1	4	yes	—
356	#95	C₂³×C₁₉	1	2	yes	—
357	#95	C₂³×C₁₉	1	2	yes	—
358	#95	C₂³×C₁₉	1	4	yes	—
359	#95	C₂³×C₁₉	1	4	yes	—
360	#95	C₂³×C₁₉	1	2	yes	—
361	#95	C₂³×C₁₉	1	2	yes	—
362	#95	C₂³×C₁₉	1	4	yes	—
363	#95	C₂³×C₁₉	1	4	yes	—
364	#95	C₂³×C₁₉	1	4	yes	—
365	#95	C₂³×C₁₉	1	4	yes	—
366	C₁₉	#34878	1	1	yes	characteristic, direct product factor, Sylow
367	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
368	C₂×Q₈	—	2	8	no	—
369	C₂×Q₈	—	2	8	no	—
370	C₂×Q₈	—	4	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	2	8	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
378	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
379	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
380	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
381	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
385	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
390	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	8	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	4	4	no	—
400	C₄⋊C₄	—	4	4	no	—
401	C₄⋊C₄	—	4	4	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	#41×C₁₉	1	8	yes	—
406	C₄²	—	2	8	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	8	no	—
409	C₄²	—	2	8	no	—
410	C₄²	—	2	8	no	—
411	C₄²	—	4	2	no	—
412	C₄²	—	4	2	no	—
413	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
414	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
415	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
416	C₄²	C₂×Q₈×C₁₉	1	4	yes	—
417	C₄²	#41×C₁₉	1	8	yes	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
421	C₂³	C₂×#41×C₁₉	1	4	yes	—
422	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
423	Q₈	—	4	16	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	16	no	—
449	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
450	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
451	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
452	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
453	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
454	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
455	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
456	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
457	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	8	no	—
461	C₂²	C₁₉×#533	1	4	yes	—
462	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
463	C₂²	C₂²×#41×C₁₉	1	2	yes	—
464	C₂²	C₂²×#41×C₁₉	1	2	yes	—
465	C₂²	C₁₉×#585	1	2	yes	—
466	C₄	—	2	2	no	—
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	8	no	—
472	C₄	—	2	8	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	4	no	—
475	C₄	—	4	4	no	—
476	C₄	—	4	4	no	—
477	C₄	C₁₉×#533	1	4	yes	—
478	C₂	—	2	4	no	—
479	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
480	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
481	C₂	C₁₉×#3458	1	1	yes	characteristic
482	C₂	C₁₉×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂⁴×C₁₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2612	C₂	semidirect
2. C₁₉×#2606	C₂	semidirect
3. C₁₉×#2605	C₂	semidirect
7. C₁₉×#2402	C₂	semidirect
8. C₁₉×#2399	C₂	semidirect
10. C₁₉×#2295	C₂	semidirect
90. C₂×C₄²×C₁₉	Q₈	semidirect
176. #34878	C₁₉	direct (N × H)
217. #2612	C₂×C₁₉	semidirect
218. #2606	C₂×C₁₉	semidirect
219. #2605	C₂×C₁₉	semidirect
223. #2402	C₂×C₁₉	semidirect
224. #2399	C₂×C₁₉	semidirect
226. #2295	C₂×C₁₉	semidirect
331. C₂×C₄²	Q₈×C₁₉	semidirect
366. C₁₉	#34878	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×#2612	2
C₁₉×#2606	2
C₁₉×#2605	2
C₁₉×#2569	2
C₁₉×#2549	2
C₁₉×#2438	2
C₁₉×#2402	2
C₁₉×#2399	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2295	2
C₁₉×#2283	2
C₄×C₁₉×#117	2
C₂×C₁₉×#376	2
#34878	19

Subgroups — C19×#34878 #18040837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34878 #18040837