Subgroups — C₁₉×#32767 #18038726

Order 4864.

778 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2621	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2620	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2074	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2073	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2072	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2016	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2015	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2013	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2001	C₂	1	2	yes	maximal, complemented
10	C₁₉×#2000	C₂	1	2	yes	maximal
11	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#103	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	C₂²	1	2	yes	—
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₁₉×#398	—	2	2	no	—
26	C₁₉×#397	—	2	2	no	—
27	C₁₉×#396	—	2	2	no	—
28	C₁₉×#394	—	2	2	no	—
29	C₁₉×#391	C₂²	1	2	yes	—
30	C₁₉×#391	C₂²	1	1	yes	characteristic
31	C₁₉×#390	C₂²	1	1	yes	characteristic
32	C₁₉×#384	C₂²	1	1	yes	characteristic
33	C₁₉×#382	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#336	C₂²	1	1	yes	characteristic
37	C₁₉×#336	C₂²	1	2	yes	—
38	C₁₉×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
41	C₂²×D₄×C₁₉	—	2	1	no	—
42	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₁₉	—	4	2	no	—
45	C₂×Q₁₆×C₁₉	—	4	2	no	—
46	C₂×Q₁₆×C₁₉	—	4	2	no	—
47	C₂×SD₁₆×C₁₉	—	4	2	no	—
48	C₂×SD₁₆×C₁₉	—	4	2	no	—
49	C₂×SD₁₆×C₁₉	—	4	2	no	—
50	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₁₉×C₄⋊Q₈	—	4	2	no	—
53	C₁₉×#124	—	4	2	no	—
54	C₁₉×C₂²⋊Q₈	—	4	2	no	—
55	C₁₉×C₂²⋊Q₈	—	4	2	no	—
56	C₁₉×C₂²⋊Q₈	—	4	2	no	—
57	C₁₉×#121	—	4	2	no	—
58	C₁₉×#117	—	4	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
73	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₁₉×#103	—	4	2	no	—
76	C₁₉×#103	—	4	2	no	—
77	C₁₉×#103	—	4	2	no	—
78	C₁₉×#102	—	4	2	no	—
79	C₁₉×C₂²⋊C₈	—	4	2	no	—
80	C₁₉×#95	—	2	2	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	4	no	—
83	C₂⁴×C₁₉	—	2	1	no	—
84	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	2	2	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	2	2	no	—
92	C₂×Q₈×C₁₉	—	2	1	no	—
93	C₂×Q₈×C₁₉	—	2	1	no	—
94	C₂×Q₈×C₁₉	—	2	2	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	1	no	—
98	C₂×D₄×C₁₉	—	2	1	no	—
99	C₂×D₄×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	—	8	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₁₉	—	4	8	no	—
115	SD₁₆×C₁₉	—	4	8	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₄⋊C₄×C₁₉	—	2	2	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	4	2	no	—
127	C₄⋊C₄×C₁₉	—	4	2	no	—
128	C₄⋊C₄×C₁₉	—	4	4	no	—
129	C₄⋊C₄×C₁₉	—	4	4	no	—
130	C₄⋊C₄×C₁₉	—	8	2	no	—
131	C₂²⋊C₄×C₁₉	—	4	2	no	—
132	C₂²⋊C₄×C₁₉	—	4	2	no	—
133	C₂²⋊C₄×C₁₉	—	4	4	no	—
134	C₂²⋊C₄×C₁₉	—	4	4	no	—
135	C₂²⋊C₄×C₁₉	—	4	2	no	—
136	C₂²⋊C₄×C₁₉	—	8	2	no	—
137	C₄²×C₁₉	—	2	2	no	—
138	C₄²×C₁₉	—	2	2	no	—
139	#32767	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₉	—	2	1	no	—
141	C₂³×C₁₉	—	2	1	no	—
142	C₂³×C₁₉	—	2	1	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	1	no	—
147	C₂³×C₁₉	—	4	1	no	—
148	C₂³×C₁₉	—	4	2	no	—
149	C₂³×C₁₉	—	4	2	no	—
150	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₁₉	—	4	2	no	—
152	Q₈×C₁₉	—	4	2	no	—
153	Q₈×C₁₉	—	4	2	no	—
154	Q₈×C₁₉	—	4	2	no	—
155	Q₈×C₁₉	—	4	2	no	—
156	Q₈×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	4	2	no	—
158	D₄×C₁₉	—	4	2	no	—
159	D₄×C₁₉	—	8	4	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	2	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	1	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	1	no	—
176	C₂×C₄×C₁₉	—	4	1	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	1	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
185	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
186	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₈×C₁₉	—	4	2	no	—
189	C₈×C₁₉	—	4	2	no	—
190	#2621	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#2620	C₂×C₁₉	1	1	yes	characteristic
192	#2074	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#2073	C₂×C₁₉	1	1	yes	characteristic, complemented
194	#2072	C₂×C₁₉	1	2	yes	complemented
195	#2016	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#2015	C₂×C₁₉	1	2	yes	complemented
197	#2013	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#2001	C₂×C₁₉	1	2	yes	complemented
199	#2000	C₂×C₁₉	1	2	yes	—
200	#1818	C₂×C₁₉	1	1	yes	characteristic, complemented
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	1	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	1	no	—
206	C₂²×C₁₉	—	8	2	no	—
207	C₂²×C₁₉	—	8	1	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	—	8	2	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	#534	1	1	yes	characteristic
212	C₂²×C₁₉	#535	1	1	yes	characteristic
213	C₂²×C₁₉	#535	1	1	yes	characteristic
214	C₂²×C₁₉	#577	1	2	yes	—
215	C₂²×C₁₉	#578	1	2	yes	—
216	C₄×C₁₉	—	4	2	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	4	1	no	—
219	C₄×C₁₉	—	8	1	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	—	8	1	no	—
223	C₄×C₁₉	—	8	2	no	—
224	C₄×C₁₉	#560	1	2	yes	—
225	C₄×C₁₉	#560	1	2	yes	—
226	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
227	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
229	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
232	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
233	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#103	C₂²×C₁₉	1	2	yes	—
235	C₂×#103	C₂²×C₁₉	1	2	yes	—
236	C₂×#103	C₂²×C₁₉	1	2	yes	—
237	C₂×#102	C₂²×C₁₉	1	2	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
239	#398	—	2	2	no	—
240	#397	—	2	2	no	—
241	#396	—	2	2	no	—
242	#394	—	2	2	no	—
243	#391	C₂²×C₁₉	1	2	yes	—
244	#391	C₂²×C₁₉	1	1	yes	characteristic
245	#390	C₂²×C₁₉	1	1	yes	characteristic
246	#384	C₂²×C₁₉	1	1	yes	characteristic
247	#382	C₂²×C₁₉	1	1	yes	characteristic
248	#340	C₂²×C₁₉	1	2	yes	—
249	#340	C₂²×C₁₉	1	2	yes	—
250	#336	C₂²×C₁₉	1	2	yes	—
251	#336	C₂²×C₁₉	1	1	yes	characteristic
252	#336	C₂²×C₁₉	1	1	yes	characteristic
253	C₂×C₁₉	—	8	1	no	—
254	C₂×C₁₉	—	16	1	no	—
255	C₂×C₁₉	#2815	1	1	yes	characteristic
256	C₂×C₁₉	#3201	1	2	yes	—
257	C₂×C₁₉	#3222	1	1	yes	characteristic
258	C₂×C₁₉	#3223	1	1	yes	characteristic
259	C₂×C₁₉	#3225	1	2	yes	—
260	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
261	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
265	C₂×Q₁₆	—	4	2	no	—
266	C₂×Q₁₆	—	4	2	no	—
267	C₂×Q₁₆	—	4	2	no	—
268	C₂×SD₁₆	—	4	2	no	—
269	C₂×SD₁₆	—	4	2	no	—
270	C₂×SD₁₆	—	4	2	no	—
271	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
272	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
273	C₄⋊Q₈	—	4	2	no	—
274	#124	—	4	2	no	—
275	C₂²⋊Q₈	—	4	2	no	—
276	C₂²⋊Q₈	—	4	2	no	—
277	C₂²⋊Q₈	—	4	2	no	—
278	#121	—	4	2	no	—
279	#117	—	4	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
294	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
296	#103	—	4	2	no	—
297	#103	—	4	2	no	—
298	#103	—	4	2	no	—
299	#102	—	4	2	no	—
300	C₂²⋊C₈	—	4	2	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	4	no	—
304	C₁₉	#32767	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁴	—	2	1	no	—
306	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	8	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
336	Q₁₆	—	4	8	no	—
337	SD₁₆	—	4	8	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄⋊C₄	—	8	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	8	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	8	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
407	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
409	C₈	—	4	2	no	—
410	C₈	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	1	no	—
421	C₂²	C₁₉×#534	1	1	yes	characteristic
422	C₂²	C₁₉×#535	1	1	yes	characteristic
423	C₂²	C₁₉×#535	1	1	yes	characteristic
424	C₂²	C₁₉×#577	1	2	yes	—
425	C₂²	C₁₉×#578	1	2	yes	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	1	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	1	no	—
433	C₄	—	8	2	no	—
434	C₄	C₁₉×#560	1	2	yes	—
435	C₄	C₁₉×#560	1	2	yes	—
436	C₂	—	8	1	no	—
437	C₂	—	16	1	no	—
438	C₂	C₁₉×#2815	1	1	yes	characteristic
439	C₂	C₁₉×#3201	1	2	yes	—
440	C₂	C₁₉×#3222	1	1	yes	characteristic
441	C₂	C₁₉×#3223	1	1	yes	characteristic
442	C₂	C₁₉×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2621	C₂	semidirect
3. C₁₉×#2074	C₂	semidirect
4. C₁₉×#2073	C₂	semidirect
5. C₁₉×#2072	C₂	semidirect
6. C₁₉×#2016	C₂	semidirect
7. C₁₉×#2015	C₂	semidirect
8. C₁₉×#2013	C₂	semidirect
9. C₁₉×#2001	C₂	semidirect
11. C₁₉×#1818	C₂	semidirect
139. #32767	C₁₉	direct (N × H)
190. #2621	C₂×C₁₉	semidirect
192. #2074	C₂×C₁₉	semidirect
193. #2073	C₂×C₁₉	semidirect
194. #2072	C₂×C₁₉	semidirect
195. #2016	C₂×C₁₉	semidirect
196. #2015	C₂×C₁₉	semidirect
197. #2013	C₂×C₁₉	semidirect
198. #2001	C₂×C₁₉	semidirect
200. #1818	C₂×C₁₉	semidirect
304. C₁₉	#32767	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×#2621	2
C₁₉×#2620	2
C₁₉×#2074	2
C₁₉×#2073	2
C₁₉×#2072	2
C₁₉×#2016	2
C₁₉×#2015	2
C₁₉×#2013	2
C₁₉×#2001	2
C₁₉×#2000	2
C₁₉×#1818	2
#32767	19

Subgroups — C19×#32767 #18038726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32767 #18038726