Subgroups — C₁₉×#34950 #18040909

Order 4864.

1796 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2586	C₂	1	4	yes	maximal
2	C₁₉×#2582	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2567	C₂	1	2	yes	maximal
4	C₁₉×#2551	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2507	C₂	1	4	yes	maximal
6	C₁₉×#2451	C₂	1	4	yes	maximal
7	C₁₉×#2399	C₂	1	4	yes	maximal
8	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₉×C₄⋊Q₈	C₂	1	4	yes	maximal
10	C₁₉×#2295	C₂	1	4	yes	maximal
11	C₄²×Q₈×C₁₉	C₂	1	2	yes	maximal
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	4	yes	—
13	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#398	C₂²	1	8	yes	—
20	C₁₉×#398	C₂²	1	4	yes	—
21	C₁₉×#398	C₂²	1	4	yes	—
22	C₁₉×#395	C₂²	1	4	yes	—
23	C₁₉×#395	C₂²	1	4	yes	—
24	C₁₉×#395	C₂²	1	8	yes	—
25	C₁₉×#391	C₂²	1	4	yes	—
26	C₁₉×#391	C₂²	1	4	yes	—
27	C₁₉×#391	C₂²	1	8	yes	—
28	C₁₉×#391	C₂²	1	2	yes	—
29	C₁₉×#389	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×#389	C₂²	1	4	yes	—
34	C₁₉×#389	C₂²	1	8	yes	—
35	C₁₉×#387	C₂²	1	8	yes	—
36	C₁₉×#387	C₂²	1	8	yes	—
37	C₁₉×#384	C₂²	1	4	yes	—
38	C₁₉×#384	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
47	C₁₉×#376	C₂²	1	4	yes	—
48	C₄³×C₁₉	C₂²	1	1	yes	characteristic
49	C₄³×C₁₉	C₂²	1	4	yes	—
50	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
51	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
52	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
53	C₁₉×C₄⋊Q₈	—	2	16	no	—
54	C₁₉×C₄⋊Q₈	—	2	4	no	—
55	C₄×Q₈×C₁₉	—	2	8	no	—
56	C₄×Q₈×C₁₉	—	2	8	no	—
57	C₄×Q₈×C₁₉	—	4	4	no	—
58	C₄×Q₈×C₁₉	—	4	8	no	—
59	C₄×Q₈×C₁₉	Q₈	1	16	yes	complemented
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
76	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
77	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
80	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×#95	C₂³	1	4	yes	—
87	C₁₉×#95	C₂³	1	8	yes	—
88	C₁₉×#95	C₂³	1	4	yes	—
89	C₁₉×#95	C₂³	1	4	yes	—
90	C₁₉×#95	C₂³	1	4	yes	—
91	C₁₉×#95	C₂³	1	4	yes	—
92	C₁₉×#95	C₂³	1	8	yes	—
93	C₁₉×#95	C₂³	1	8	yes	—
94	C₁₉×#95	C₂³	1	8	yes	—
95	C₂×Q₈×C₁₉	—	2	4	no	—
96	C₂×Q₈×C₁₉	—	2	4	no	—
97	C₂×Q₈×C₁₉	—	2	16	no	—
98	C₂×Q₈×C₁₉	—	2	4	no	—
99	C₂×Q₈×C₁₉	—	4	4	no	—
100	C₂×Q₈×C₁₉	—	4	2	no	—
101	C₂×Q₈×C₁₉	—	4	2	no	—
102	C₂×Q₈×C₁₉	C₂×Q₈	1	8	yes	—
103	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₁₉	—	2	8	no	—
115	C₄⋊C₄×C₁₉	—	2	8	no	—
116	C₄⋊C₄×C₁₉	—	2	4	no	—
117	C₄⋊C₄×C₁₉	—	2	16	no	—
118	C₄⋊C₄×C₁₉	—	2	8	no	—
119	C₄⋊C₄×C₁₉	—	2	8	no	—
120	C₄⋊C₄×C₁₉	—	4	8	no	—
121	C₄⋊C₄×C₁₉	—	4	8	no	—
122	C₄⋊C₄×C₁₉	—	4	2	no	—
123	C₄⋊C₄×C₁₉	—	4	4	no	—
124	C₄⋊C₄×C₁₉	—	4	4	no	—
125	C₄⋊C₄×C₁₉	C₂×Q₈	1	16	yes	—
126	C₄⋊C₄×C₁₉	C₂×Q₈	1	8	yes	—
127	C₄⋊C₄×C₁₉	#41	1	8	yes	—
128	C₄²×C₁₉	—	2	8	no	—
129	C₄²×C₁₉	—	2	4	no	—
130	C₄²×C₁₉	—	2	8	no	—
131	C₄²×C₁₉	—	2	8	no	—
132	C₄²×C₁₉	—	2	2	no	—
133	C₄²×C₁₉	—	2	8	no	—
134	C₄²×C₁₉	—	2	8	no	—
135	C₄²×C₁₉	—	4	1	no	—
136	C₄²×C₁₉	—	4	4	no	—
137	C₄²×C₁₉	C₂×Q₈	1	16	yes	—
138	C₄²×C₁₉	C₂×Q₈	1	8	yes	—
139	C₄²×C₁₉	#41	1	4	yes	—
140	#34950	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
142	Q₈×C₁₉	—	2	16	no	—
143	Q₈×C₁₉	—	4	16	no	—
144	Q₈×C₁₉	—	4	8	no	—
145	C₂×C₄×C₁₉	—	2	2	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	1	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	8	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
166	C₂×C₄×C₁₉	C₂²×Q₈	1	8	yes	—
167	C₂×C₄×C₁₉	C₂²×Q₈	1	8	yes	—
168	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
169	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
170	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
171	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
173	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
174	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
175	#2586	C₂×C₁₉	1	4	yes	—
176	#2582	C₂×C₁₉	1	1	yes	characteristic
177	#2567	C₂×C₁₉	1	2	yes	—
178	#2551	C₂×C₁₉	1	1	yes	characteristic
179	#2507	C₂×C₁₉	1	4	yes	—
180	#2451	C₂×C₁₉	1	4	yes	—
181	#2399	C₂×C₁₉	1	4	yes	—
182	C₄×C₄⋊Q₈	C₂×C₁₉	1	4	yes	—
183	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
184	#2295	C₂×C₁₉	1	4	yes	—
185	C₄²×Q₈	C₂×C₁₉	1	2	yes	—
186	C₂²×C₁₉	C₂³×Q₈	1	2	yes	—
187	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
188	C₂²×C₁₉	C₂²×#41	1	2	yes	—
189	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
190	C₂²×C₁₉	#585	1	1	yes	characteristic
191	C₄×C₁₉	—	2	8	no	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	4	no	—
194	C₄×C₁₉	—	2	8	no	—
195	C₄×C₁₉	—	2	8	no	—
196	C₄×C₁₉	—	4	4	no	—
197	C₄×C₁₉	—	4	4	no	—
198	C₄×C₁₉	—	4	1	no	—
199	C₄×C₁₉	—	4	4	no	—
200	C₄×C₁₉	#533	1	8	yes	—
201	C₄×C₁₉	Q₈²	1	4	yes	—
202	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
203	C₂×C₄⋊Q₈	C₂²×C₁₉	1	4	yes	—
204	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
205	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
206	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
207	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
208	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
209	#398	C₂²×C₁₉	1	4	yes	—
210	#398	C₂²×C₁₉	1	8	yes	—
211	#398	C₂²×C₁₉	1	4	yes	—
212	#395	C₂²×C₁₉	1	8	yes	—
213	#395	C₂²×C₁₉	1	4	yes	—
214	#395	C₂²×C₁₉	1	4	yes	—
215	#391	C₂²×C₁₉	1	2	yes	—
216	#391	C₂²×C₁₉	1	8	yes	—
217	#391	C₂²×C₁₉	1	4	yes	—
218	#391	C₂²×C₁₉	1	4	yes	—
219	#389	C₂²×C₁₉	1	4	yes	—
220	#389	C₂²×C₁₉	1	4	yes	—
221	#389	C₂²×C₁₉	1	8	yes	—
222	#389	C₂²×C₁₉	1	4	yes	—
223	#389	C₂²×C₁₉	1	4	yes	—
224	#389	C₂²×C₁₉	1	4	yes	—
225	#387	C₂²×C₁₉	1	8	yes	—
226	#387	C₂²×C₁₉	1	8	yes	—
227	#384	C₂²×C₁₉	1	4	yes	—
228	#384	C₂²×C₁₉	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
230	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
231	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
232	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
233	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
234	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
235	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
236	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
237	#376	C₂²×C₁₉	1	4	yes	—
238	C₄³	C₂²×C₁₉	1	1	yes	characteristic
239	C₄³	C₂²×C₁₉	1	4	yes	—
240	C₂×C₁₉	C₂×#533	1	2	yes	—
241	C₂×C₁₉	#3460	1	1	yes	characteristic
242	C₂×C₁₉	C₂×Q₈²	1	1	yes	characteristic
243	C₂×C₁₉	Q₈×#41	1	2	yes	—
244	C₂×C₁₉	#3481	1	1	yes	characteristic
245	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
246	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
247	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
248	C₄⋊Q₈	—	2	16	no	—
249	C₄⋊Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	8	no	—
251	C₄×Q₈	—	2	8	no	—
252	C₄×Q₈	—	4	8	no	—
253	C₄×Q₈	—	4	4	no	—
254	C₄×Q₈	Q₈×C₁₉	1	16	yes	complemented
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
259	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
261	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
266	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
269	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
270	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
272	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
274	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
275	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
276	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
278	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
279	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
280	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
281	#95	C₂³×C₁₉	1	4	yes	—
282	#95	C₂³×C₁₉	1	8	yes	—
283	#95	C₂³×C₁₉	1	4	yes	—
284	#95	C₂³×C₁₉	1	4	yes	—
285	#95	C₂³×C₁₉	1	4	yes	—
286	#95	C₂³×C₁₉	1	4	yes	—
287	#95	C₂³×C₁₉	1	8	yes	—
288	#95	C₂³×C₁₉	1	8	yes	—
289	#95	C₂³×C₁₉	1	8	yes	—
290	C₁₉	#34950	1	1	yes	characteristic, direct product factor, Sylow
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	16	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	C₂×Q₈×C₁₉	1	8	yes	—
299	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
300	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
301	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
302	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
303	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
304	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
305	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
306	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
307	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
308	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	—	4	8	no	—
317	C₄⋊C₄	—	4	8	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	4	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	C₂×Q₈×C₁₉	1	16	yes	—
322	C₄⋊C₄	C₂×Q₈×C₁₉	1	8	yes	—
323	C₄⋊C₄	#41×C₁₉	1	8	yes	—
324	C₄²	—	2	8	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	8	no	—
327	C₄²	—	2	8	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	8	no	—
330	C₄²	—	2	8	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	4	no	—
333	C₄²	C₂×Q₈×C₁₉	1	16	yes	—
334	C₄²	C₂×Q₈×C₁₉	1	8	yes	—
335	C₄²	#41×C₁₉	1	4	yes	—
336	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
337	Q₈	—	2	16	no	—
338	Q₈	—	4	16	no	—
339	Q₈	—	4	8	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
361	C₂×C₄	C₂²×Q₈×C₁₉	1	8	yes	—
362	C₂×C₄	C₂²×Q₈×C₁₉	1	8	yes	—
363	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
364	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
365	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
366	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
367	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
368	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
369	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
370	C₂²	C₂³×Q₈×C₁₉	1	2	yes	—
371	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
372	C₂²	C₂²×#41×C₁₉	1	2	yes	—
373	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂²	C₁₉×#585	1	1	yes	characteristic
375	C₄	—	2	8	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	4	no	—
378	C₄	—	2	8	no	—
379	C₄	—	2	8	no	—
380	C₄	—	4	4	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	4	no	—
383	C₄	—	4	1	no	—
384	C₄	C₁₉×#533	1	8	yes	—
385	C₄	Q₈²×C₁₉	1	4	yes	—
386	C₂	C₂×C₁₉×#533	1	2	yes	—
387	C₂	C₁₉×#3460	1	1	yes	characteristic
388	C₂	C₂×Q₈²×C₁₉	1	1	yes	characteristic
389	C₂	Q₈×#41×C₁₉	1	2	yes	—
390	C₂	C₁₉×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle, prime radical	C₂³×C₁₉	C₂⁵
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
59. C₄×Q₈×C₁₉	Q₈	semidirect
140. #34950	C₁₉	direct (N × H)
254. C₄×Q₈	Q₈×C₁₉	semidirect
290. C₁₉	#34950	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×#2586	2
C₁₉×#2582	2
C₁₉×#2567	2
C₁₉×#2551	2
C₁₉×#2507	2
C₁₉×#2451	2
C₁₉×#2399	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#2295	2
C₄²×Q₈×C₁₉	2
#34950	19

Subgroups — C19×#34950 #18040909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34950 #18040909