Subgroups — C₁₉×#32761 #18038720

Order 4864.

838 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2850	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2074	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2072	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2071	C₂	1	1	yes	maximal, characteristic, 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×#1817	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	C₂²×C₄²×C₁₉	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×#391	C₂²	1	2	yes	—
26	C₁₉×#391	C₂²	1	1	yes	characteristic
27	C₁₉×#390	C₂²	1	1	yes	characteristic
28	C₁₉×#389	—	2	1	no	—
29	C₁₉×#389	—	2	1	no	—
30	C₁₉×#388	—	2	1	no	—
31	C₁₉×#388	—	2	1	no	—
32	C₁₉×#386	—	2	1	no	—
33	C₁₉×#386	—	2	1	no	—
34	C₁₉×#384	C₂²	1	1	yes	characteristic
35	C₁₉×#382	C₂²	1	1	yes	characteristic
36	C₁₉×#380	—	2	1	no	—
37	C₁₉×#380	—	2	1	no	—
38	C₁₉×#340	C₂²	1	2	yes	—
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#336	C₂²	1	1	yes	characteristic
41	C₁₉×#336	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×Q₁₆×C₁₉	—	4	2	no	—
51	C₂×Q₁₆×C₁₉	—	4	2	no	—
52	C₂×Q₁₆×C₁₉	—	4	2	no	—
53	C₂×SD₁₆×C₁₉	—	4	2	no	—
54	C₂×SD₁₆×C₁₉	—	4	2	no	—
55	C₂×SD₁₆×C₁₉	—	4	2	no	—
56	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
58	C₁₉×C₄⋊Q₈	—	4	2	no	—
59	C₁₉×#124	—	4	2	no	—
60	C₁₉×C₂²⋊Q₈	—	4	2	no	—
61	C₁₉×C₂²⋊Q₈	—	4	2	no	—
62	C₁₉×C₂²⋊Q₈	—	4	2	no	—
63	C₁₉×#121	—	4	2	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	1	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄²×C₁₉	—	4	2	no	—
81	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×#103	—	4	2	no	—
86	C₁₉×#103	—	4	2	no	—
87	C₁₉×#103	—	4	2	no	—
88	C₁₉×#102	—	4	2	no	—
89	C₁₉×C₂²⋊C₈	—	4	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₁₉×#95	—	2	1	no	—
94	C₁₉×#95	—	2	1	no	—
95	C₁₉×#95	—	2	1	no	—
96	C₂⁴×C₁₉	—	2	1	no	—
97	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	2	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	4	2	no	—
113	C₂×D₄×C₁₉	—	4	2	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₁₉	—	4	8	no	—
137	SD₁₆×C₁₉	—	4	8	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	4	2	no	—
149	C₄⋊C₄×C₁₉	—	4	2	no	—
150	C₄⋊C₄×C₁₉	—	4	4	no	—
151	C₄⋊C₄×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	—	4	2	no	—
153	C₄⋊C₄×C₁₉	—	4	2	no	—
154	C₂²⋊C₄×C₁₉	—	4	2	no	—
155	C₂²⋊C₄×C₁₉	—	4	2	no	—
156	C₂²⋊C₄×C₁₉	—	4	2	no	—
157	C₂²⋊C₄×C₁₉	—	4	4	no	—
158	C₂²⋊C₄×C₁₉	—	4	2	no	—
159	C₂²⋊C₄×C₁₉	—	4	2	no	—
160	C₂²⋊C₄×C₁₉	—	4	2	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	2	2	no	—
163	C₄²×C₁₉	—	4	1	no	—
164	C₄²×C₁₉	—	4	1	no	—
165	#32761	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	1	no	—
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	2	1	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	1	no	—
176	C₂³×C₁₉	—	4	1	no	—
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	—	4	1	no	—
179	C₂³×C₁₉	#137	1	2	yes	—
180	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₁₉	—	4	2	no	—
182	Q₈×C₁₉	—	4	2	no	—
183	Q₈×C₁₉	—	4	2	no	—
184	Q₈×C₁₉	—	4	2	no	—
185	Q₈×C₁₉	—	4	2	no	—
186	Q₈×C₁₉	—	4	2	no	—
187	D₄×C₁₉	—	4	2	no	—
188	D₄×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	8	4	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	4	4	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	2	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	#135	1	2	yes	—
223	C₂×C₄×C₁₉	#137	1	2	yes	—
224	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
225	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
228	C₈×C₁₉	—	4	2	no	—
229	C₈×C₁₉	—	4	2	no	—
230	#2857	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#2850	C₂×C₁₉	1	1	yes	characteristic
232	#2074	C₂×C₁₉	1	2	yes	complemented
233	#2072	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#2071	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#2016	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#2015	C₂×C₁₉	1	2	yes	complemented
237	#2013	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#2001	C₂×C₁₉	1	2	yes	complemented
239	#2000	C₂×C₁₉	1	2	yes	—
240	#1817	C₂×C₁₉	1	1	yes	characteristic, complemented
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	4	1	no	—
245	C₂²×C₁₉	—	4	1	no	—
246	C₂²×C₁₉	—	4	1	no	—
247	C₂²×C₁₉	—	4	1	no	—
248	C₂²×C₁₉	—	8	1	no	—
249	C₂²×C₁₉	—	8	1	no	—
250	C₂²×C₁₉	—	8	1	no	—
251	C₂²×C₁₉	—	8	1	no	—
252	C₂²×C₁₉	—	8	1	no	—
253	C₂²×C₁₉	—	8	1	no	—
254	C₂²×C₁₉	—	8	1	no	—
255	C₂²×C₁₉	#534	1	1	yes	characteristic
256	C₂²×C₁₉	#535	1	1	yes	characteristic
257	C₂²×C₁₉	#535	1	1	yes	characteristic
258	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
259	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
261	C₂²×C₁₉	#575	1	1	yes	characteristic
262	C₄×C₁₉	—	2	2	no	—
263	C₄×C₁₉	—	2	2	no	—
264	C₄×C₁₉	—	4	1	no	—
265	C₄×C₁₉	—	4	1	no	—
266	C₄×C₁₉	—	4	1	no	—
267	C₄×C₁₉	—	8	1	no	—
268	C₄×C₁₉	—	8	2	no	—
269	C₄×C₁₉	—	8	1	no	—
270	C₄×C₁₉	—	8	1	no	—
271	C₄×C₁₉	—	8	2	no	—
272	C₄×C₁₉	#560	1	2	yes	—
273	C₄×C₁₉	#560	1	2	yes	—
274	C₂²×Q₁₆	C₂²×C₁₉	1	2	yes	—
275	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
276	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
278	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
279	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
280	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
281	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
282	C₂×#103	C₂²×C₁₉	1	2	yes	—
283	C₂×#103	C₂²×C₁₉	1	2	yes	—
284	C₂×#103	C₂²×C₁₉	1	2	yes	—
285	C₂×#102	C₂²×C₁₉	1	2	yes	—
286	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
287	#391	C₂²×C₁₉	1	1	yes	characteristic
288	#391	C₂²×C₁₉	1	2	yes	—
289	#390	C₂²×C₁₉	1	1	yes	characteristic
290	#389	—	2	1	no	—
291	#389	—	2	1	no	—
292	#388	—	2	1	no	—
293	#388	—	2	1	no	—
294	#386	—	2	1	no	—
295	#386	—	2	1	no	—
296	#384	C₂²×C₁₉	1	1	yes	characteristic
297	#382	C₂²×C₁₉	1	1	yes	characteristic
298	#380	—	2	1	no	—
299	#380	—	2	1	no	—
300	#340	C₂²×C₁₉	1	2	yes	—
301	#340	C₂²×C₁₉	1	2	yes	—
302	#336	C₂²×C₁₉	1	1	yes	characteristic
303	#336	C₂²×C₁₉	1	1	yes	characteristic
304	#336	C₂²×C₁₉	1	2	yes	—
305	C₂×C₁₉	—	4	2	no	—
306	C₂×C₁₉	—	16	1	no	—
307	C₂×C₁₉	#2815	1	1	yes	characteristic
308	C₂×C₁₉	#3190	1	1	yes	characteristic
309	C₂×C₁₉	#3196	1	1	yes	characteristic
310	C₂×C₁₉	#3210	1	1	yes	characteristic
311	C₂×C₁₉	#3212	1	1	yes	characteristic
312	C₂×C₁₉	#3215	1	1	yes	characteristic
313	C₂×C₁₉	#3218	1	1	yes	characteristic
314	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
318	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
319	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
321	C₂×Q₁₆	—	4	2	no	—
322	C₂×Q₁₆	—	4	2	no	—
323	C₂×Q₁₆	—	4	2	no	—
324	C₂×SD₁₆	—	4	2	no	—
325	C₂×SD₁₆	—	4	2	no	—
326	C₂×SD₁₆	—	4	2	no	—
327	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
328	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
329	C₄⋊Q₈	—	4	2	no	—
330	#124	—	4	2	no	—
331	C₂²⋊Q₈	—	4	2	no	—
332	C₂²⋊Q₈	—	4	2	no	—
333	C₂²⋊Q₈	—	4	2	no	—
334	#121	—	4	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₂²⋊C₄	—	2	1	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₄²	—	4	2	no	—
352	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
353	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
356	#103	—	4	2	no	—
357	#103	—	4	2	no	—
358	#103	—	4	2	no	—
359	#102	—	4	2	no	—
360	C₂²⋊C₈	—	4	2	no	—
361	#95	—	2	2	no	—
362	#95	—	2	2	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	C₁₉	#32761	1	1	yes	characteristic, direct product factor, Sylow
368	C₂⁴	—	2	1	no	—
369	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	1	no	—
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×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
408	Q₁₆	—	4	8	no	—
409	SD₁₆	—	4	8	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	4	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	—	4	4	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	—	4	4	no	—
430	C₂²⋊C₄	—	4	2	no	—
431	C₂²⋊C₄	—	4	2	no	—
432	C₂²⋊C₄	—	4	2	no	—
433	C₄²	—	2	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	4	1	no	—
436	C₄²	—	4	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	1	no	—
445	C₂³	—	4	1	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	C₁₉×#137	1	2	yes	—
451	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
452	Q₈	—	4	2	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	8	4	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	C₁₉×#135	1	2	yes	—
494	C₂×C₄	C₁₉×#137	1	2	yes	—
495	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
496	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
497	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
498	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
499	C₈	—	4	2	no	—
500	C₈	—	4	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	2	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	8	1	no	—
510	C₂²	—	8	1	no	—
511	C₂²	—	8	1	no	—
512	C₂²	—	8	1	no	—
513	C₂²	—	8	1	no	—
514	C₂²	—	8	1	no	—
515	C₂²	C₁₉×#534	1	1	yes	characteristic
516	C₂²	C₁₉×#535	1	1	yes	characteristic
517	C₂²	C₁₉×#535	1	1	yes	characteristic
518	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
519	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
520	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
521	C₂²	C₁₉×#575	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	8	1	no	—
528	C₄	—	8	2	no	—
529	C₄	—	8	1	no	—
530	C₄	—	8	1	no	—
531	C₄	—	8	2	no	—
532	C₄	C₁₉×#560	1	2	yes	—
533	C₄	C₁₉×#560	1	2	yes	—
534	C₂	—	4	2	no	—
535	C₂	—	16	1	no	—
536	C₂	C₁₉×#2815	1	1	yes	characteristic
537	C₂	C₁₉×#3190	1	1	yes	characteristic
538	C₂	C₁₉×#3196	1	1	yes	characteristic
539	C₂	C₁₉×#3210	1	1	yes	characteristic
540	C₂	C₁₉×#3212	1	1	yes	characteristic
541	C₂	C₁₉×#3215	1	1	yes	characteristic
542	C₂	C₁₉×#3218	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2857	C₂	semidirect
3. C₁₉×#2074	C₂	semidirect
4. C₁₉×#2072	C₂	semidirect
5. C₁₉×#2071	C₂	semidirect
6. C₁₉×#2016	C₂	semidirect
7. C₁₉×#2015	C₂	semidirect
8. C₁₉×#2013	C₂	semidirect
9. C₁₉×#2001	C₂	semidirect
11. C₁₉×#1817	C₂	semidirect
165. #32761	C₁₉	direct (N × H)
230. #2857	C₂×C₁₉	semidirect
232. #2074	C₂×C₁₉	semidirect
233. #2072	C₂×C₁₉	semidirect
234. #2071	C₂×C₁₉	semidirect
235. #2016	C₂×C₁₉	semidirect
236. #2015	C₂×C₁₉	semidirect
237. #2013	C₂×C₁₉	semidirect
238. #2001	C₂×C₁₉	semidirect
240. #1817	C₂×C₁₉	semidirect
367. C₁₉	#32761	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×#2857	2
C₁₉×#2850	2
C₁₉×#2074	2
C₁₉×#2072	2
C₁₉×#2071	2
C₁₉×#2016	2
C₁₉×#2015	2
C₁₉×#2013	2
C₁₉×#2001	2
C₁₉×#2000	2
C₁₉×#1817	2
#32761	19

Subgroups — C19×#32761 #18038720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32761 #18038720