Subgroups — C₁₉×#32711 #18038670

Order 4864.

984 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2848	C₂	1	2	yes	maximal
2	C₁₉×#2077	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2075	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2036	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2035	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2035	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2001	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
17	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
18	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
19	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₁₉×#385	—	2	2	no	—
25	C₁₉×#385	—	2	2	no	—
26	C₁₉×#385	—	2	2	no	—
27	C₁₉×#380	C₂²	1	2	yes	—
28	C₁₉×#380	C₂²	1	2	yes	—
29	C₁₉×#380	C₂²	1	2	yes	—
30	C₁₉×#379	—	2	2	no	—
31	C₁₉×#340	C₂²	1	2	yes	complemented
32	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#340	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#340	C₂²	1	2	yes	complemented
35	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₉	—	4	2	no	—
38	C₂³×C₄×C₁₉	—	4	1	no	—
39	C₂³×C₄×C₁₉	—	4	2	no	—
40	C₂³×C₄×C₁₉	—	4	1	no	—
41	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂×Q₁₆×C₁₉	—	4	2	no	—
46	C₂×Q₁₆×C₁₉	—	4	1	no	—
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×C₂²⋊Q₈	—	4	2	no	—
51	C₁₉×C₂²⋊Q₈	—	4	2	no	—
52	C₁₉×C₂²⋊Q₈	—	4	2	no	—
53	C₁₉×C₂²⋊Q₈	—	4	2	no	—
54	C₁₉×C₂²⋊Q₈	—	4	2	no	—
55	C₁₉×C₂²⋊Q₈	—	4	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₁₉×#107	—	4	1	no	—
69	C₁₉×#106	—	4	2	no	—
70	C₁₉×#103	—	4	2	no	—
71	C₁₉×#103	—	4	2	no	—
72	C₁₉×#103	—	4	2	no	—
73	C₁₉×C₂²⋊C₈	—	4	2	no	—
74	C₁₉×C₂²⋊C₈	—	4	1	no	—
75	C₁₉×C₂²⋊C₈	—	4	1	no	—
76	C₁₉×C₂²⋊C₈	—	4	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	4	no	—
82	C₂⁴×C₁₉	—	4	2	no	—
83	C₂⁴×C₁₉	—	4	1	no	—
84	C₂⁴×C₁₉	—	4	1	no	—
85	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
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	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	2	2	no	—
95	C₂²×C₄×C₁₉	—	2	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	1	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	4	no	—
113	C₂²×C₄×C₁₉	—	4	8	no	—
114	C₂²×C₄×C₁₉	—	4	4	no	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₁₉	—	4	4	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	1	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	2	2	no	—
131	C₄⋊C₄×C₁₉	—	2	2	no	—
132	C₄⋊C₄×C₁₉	—	4	4	no	—
133	C₄⋊C₄×C₁₉	—	4	4	no	—
134	C₄⋊C₄×C₁₉	—	4	4	no	—
135	C₂²⋊C₄×C₁₉	—	4	4	no	—
136	C₂²⋊C₄×C₁₉	—	4	4	no	—
137	C₂²⋊C₄×C₁₉	—	4	4	no	—
138	C₂²⋊C₄×C₁₉	—	4	4	no	—
139	C₂²⋊C₄×C₁₉	—	4	4	no	—
140	C₂²⋊C₄×C₁₉	—	4	4	no	—
141	#32711	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	1	no	—
147	C₂³×C₁₉	—	2	2	no	—
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	2	1	no	—
152	C₂³×C₁₉	—	4	8	no	—
153	C₂³×C₁₉	—	4	4	no	—
154	C₂³×C₁₉	—	4	4	no	—
155	C₂³×C₁₉	—	4	8	no	—
156	C₂³×C₁₉	—	4	4	no	—
157	C₂³×C₁₉	#135	1	2	yes	—
158	C₂³×C₁₉	#137	1	4	yes	—
159	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₁₉	—	4	2	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	Q₈×C₁₉	—	4	2	no	—
163	Q₈×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	2	2	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	1	no	—
169	C₂×C₄×C₁₉	—	4	8	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	1	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	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	2	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	—	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	H(5,𝔽₂)	1	2	yes	—
191	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
192	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
193	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
194	C₈×C₁₉	—	4	2	no	—
195	C₈×C₁₉	—	4	1	no	—
196	C₈×C₁₉	—	4	1	no	—
197	#2848	C₂×C₁₉	1	2	yes	—
198	#2077	C₂×C₁₉	1	2	yes	complemented
199	#2075	C₂×C₁₉	1	1	yes	characteristic, complemented
200	#2036	C₂×C₁₉	1	2	yes	complemented
201	#2035	C₂×C₁₉	1	2	yes	complemented
202	#2035	C₂×C₁₉	1	2	yes	complemented
203	#2001	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#2001	C₂×C₁₉	1	2	yes	complemented
205	#1779	C₂×C₁₉	1	1	yes	characteristic
206	C₂²×C₁₉	—	2	4	no	—
207	C₂²×C₁₉	—	2	4	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	2	4	no	—
211	C₂²×C₁₉	—	4	16	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	4	2	no	—
214	C₂²×C₁₉	—	4	1	no	—
215	C₂²×C₁₉	—	4	2	no	—
216	C₂²×C₁₉	—	4	2	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	#534	1	2	yes	—
220	C₂²×C₁₉	#534	1	1	yes	characteristic
221	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
222	C₂²×C₁₉	C₂×#137	1	2	yes	—
223	C₂²×C₁₉	#575	1	1	yes	characteristic
224	C₄×C₁₉	—	4	1	no	—
225	C₄×C₁₉	—	4	2	no	—
226	C₄×C₁₉	—	8	2	no	—
227	C₄×C₁₉	—	8	2	no	—
228	C₄×C₁₉	—	8	2	no	—
229	C₄×C₁₉	—	8	2	no	—
230	C₄×C₁₉	#560	1	2	yes	—
231	C₄×C₁₉	#560	1	1	yes	characteristic
232	C₄×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
234	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
235	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
236	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
237	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
238	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
239	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
240	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
241	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
242	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
243	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
245	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
246	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
247	#385	—	2	2	no	—
248	#385	—	2	2	no	—
249	#385	—	2	2	no	—
250	#380	C₂²×C₁₉	1	2	yes	—
251	#380	C₂²×C₁₉	1	2	yes	—
252	#380	C₂²×C₁₉	1	2	yes	—
253	#379	—	2	2	no	—
254	#340	C₂²×C₁₉	1	2	yes	complemented
255	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
256	#340	C₂²×C₁₉	1	1	yes	characteristic, complemented
257	#340	C₂²×C₁₉	1	2	yes	complemented
258	C₂×C₁₉	—	4	2	no	—
259	C₂×C₁₉	—	4	4	no	—
260	C₂×C₁₉	#2812	1	1	yes	characteristic
261	C₂×C₁₉	#3190	1	2	yes	—
262	C₂×C₁₉	#3191	1	1	yes	characteristic
263	C₂×C₁₉	#3195	1	1	yes	characteristic
264	C₂×C₁₉	#3196	1	2	yes	—
265	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
267	C₂³×C₄	—	4	2	no	—
268	C₂³×C₄	—	4	1	no	—
269	C₂³×C₄	—	4	2	no	—
270	C₂³×C₄	—	4	1	no	—
271	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
272	C₂³×C₄	D₄×C₁₉	1	2	yes	—
273	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
275	C₂×Q₁₆	—	4	2	no	—
276	C₂×Q₁₆	—	4	1	no	—
277	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
279	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
280	C₂²⋊Q₈	—	4	2	no	—
281	C₂²⋊Q₈	—	4	2	no	—
282	C₂²⋊Q₈	—	4	2	no	—
283	C₂²⋊Q₈	—	4	2	no	—
284	C₂²⋊Q₈	—	4	2	no	—
285	C₂²⋊Q₈	—	4	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	#107	—	4	1	no	—
299	#106	—	4	2	no	—
300	#103	—	4	2	no	—
301	#103	—	4	2	no	—
302	#103	—	4	2	no	—
303	C₂²⋊C₈	—	4	1	no	—
304	C₂²⋊C₈	—	4	2	no	—
305	C₂²⋊C₈	—	4	2	no	—
306	C₂²⋊C₈	—	4	1	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	C₁₉	#32711	1	1	yes	characteristic, direct product factor, Sylow
311	C₂⁴	—	2	2	no	—
312	C₂⁴	—	2	4	no	—
313	C₂⁴	—	4	2	no	—
314	C₂⁴	—	4	1	no	—
315	C₂⁴	—	4	1	no	—
316	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	8	no	—
344	C₂²×C₄	—	4	4	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
349	Q₁₆	—	4	4	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₂²⋊C₄	—	4	4	no	—
369	C₂²⋊C₄	—	4	4	no	—
370	C₂²⋊C₄	—	4	4	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	4	8	no	—
383	C₂³	—	4	4	no	—
384	C₂³	—	4	4	no	—
385	C₂³	—	4	8	no	—
386	C₂³	—	4	4	no	—
387	C₂³	C₁₉×#135	1	2	yes	—
388	C₂³	C₁₉×#137	1	4	yes	—
389	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
390	Q₈	—	4	2	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
421	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
423	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
424	C₈	—	4	2	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	4	16	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	2	no	—
440	C₂²	C₁₉×#534	1	2	yes	—
441	C₂²	C₁₉×#534	1	1	yes	characteristic
442	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
443	C₂²	C₂×C₁₉×#137	1	2	yes	—
444	C₂²	C₁₉×#575	1	1	yes	characteristic
445	C₄	—	4	1	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	2	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	2	no	—
451	C₄	C₁₉×#560	1	2	yes	—
452	C₄	C₁₉×#560	1	1	yes	characteristic
453	C₄	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
454	C₂	—	4	2	no	—
455	C₂	—	4	4	no	—
456	C₂	C₁₉×#2812	1	1	yes	characteristic
457	C₂	C₁₉×#3190	1	2	yes	—
458	C₂	C₁₉×#3191	1	1	yes	characteristic
459	C₂	C₁₉×#3195	1	1	yes	characteristic
460	C₂	C₁₉×#3196	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2077	C₂	semidirect
3. C₁₉×#2075	C₂	semidirect
4. C₁₉×#2036	C₂	semidirect
5. C₁₉×#2035	C₂	semidirect
6. C₁₉×#2035	C₂	semidirect
7. C₁₉×#2001	C₂	semidirect
8. C₁₉×#2001	C₂	semidirect
11. C₂²×Q₁₆×C₁₉	C₂²	semidirect
15. C₂×C₁₉×#107	C₂²	semidirect
16. C₂×C₁₉×#106	C₂²	semidirect
17. C₂×C₁₉×#103	C₂²	semidirect
18. C₂×C₁₉×#103	C₂²	semidirect
19. C₂×C₁₉×#103	C₂²	semidirect
31. C₁₉×#340	C₂²	semidirect
32. C₁₉×#340	C₂²	semidirect
33. C₁₉×#340	C₂²	semidirect
34. C₁₉×#340	C₂²	semidirect
141. #32711	C₁₉	direct (N × H)
198. #2077	C₂×C₁₉	semidirect
199. #2075	C₂×C₁₉	semidirect
200. #2036	C₂×C₁₉	semidirect
201. #2035	C₂×C₁₉	semidirect
202. #2035	C₂×C₁₉	semidirect
203. #2001	C₂×C₁₉	semidirect
204. #2001	C₂×C₁₉	semidirect
234. C₂²×Q₁₆	C₂²×C₁₉	semidirect
238. C₂×#107	C₂²×C₁₉	semidirect
239. C₂×#106	C₂²×C₁₉	semidirect
240. C₂×#103	C₂²×C₁₉	semidirect
241. C₂×#103	C₂²×C₁₉	semidirect
242. C₂×#103	C₂²×C₁₉	semidirect
254. #340	C₂²×C₁₉	semidirect
255. #340	C₂²×C₁₉	semidirect
256. #340	C₂²×C₁₉	semidirect
257. #340	C₂²×C₁₉	semidirect
310. C₁₉	#32711	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×#2848	2
C₁₉×#2077	2
C₁₉×#2075	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#2001	2
C₁₉×#1779	2
#32711	19

Subgroups — C19×#32711 #18038670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32711 #18038670