Subgroups — C₁₉×#21945 #18027904

Order 4864.

1010 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#408	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2311	C₂	1	2	yes	maximal
3	C₁₉×#1854	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1854	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1853	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1852	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1809	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1807	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#117	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#107	C₂²	1	2	yes	—
16	C₂×C₁₉×#107	C₂²	1	2	yes	—
17	C₂×C₁₉×#106	C₂²	1	2	yes	—
18	C₂×C₁₉×#106	C₂²	1	2	yes	—
19	C₁₉×#408	C₄	1	8	yes	complemented
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₁₉×#391	—	2	2	no	—
23	C₁₉×#390	—	2	2	no	—
24	C₁₉×#386	—	2	2	no	—
25	C₁₉×#386	—	2	2	no	—
26	C₁₉×#380	C₂²	1	2	yes	—
27	C₁₉×#380	C₂²	1	2	yes	—
28	C₁₉×#380	C₂²	1	2	yes	—
29	C₁₉×#380	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	1	yes	characteristic
31	C₁₉×#340	C₂²	1	1	yes	characteristic
32	C₁₉×#340	C₂²	1	1	yes	characteristic
33	C₁₉×#340	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₂×#41×C₁₉	—	4	2	no	—
37	C₂×#41×C₁₉	—	4	2	no	—
38	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
39	C₂×#41×C₁₉	Q₈	1	4	yes	—
40	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	—	2	2	no	—
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂×M₁₆×C₁₉	—	4	2	no	—
47	C₂×M₁₆×C₁₉	C₂×C₄	1	4	yes	complemented
48	C₂²×C₈×C₁₉	—	4	2	no	—
49	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×#117	—	4	2	no	—
54	C₁₉×#117	—	4	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
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×C₄²×C₁₉	—	2	2	no	—
68	C₁₉×#107	—	4	2	no	—
69	C₁₉×#107	—	4	2	no	—
70	C₁₉×#106	—	4	2	no	—
71	C₁₉×#106	—	4	2	no	—
72	C₁₉×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
73	C₁₉×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
80	#41×C₁₉	—	4	4	no	—
81	#41×C₁₉	—	4	4	no	—
82	#41×C₁₉	—	4	8	no	—
83	C₂×Q₈×C₁₉	—	4	2	no	—
84	C₂×Q₈×C₁₉	C₄⋊C₄	1	4	yes	—
85	C₂×D₄×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	—	4	2	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
89	C₂×D₄×C₁₉	C₄⋊C₄	1	8	yes	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×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	—	4	4	no	—
101	C₂²×C₄×C₁₉	—	8	2	no	—
102	C₂²×C₄×C₁₉	—	8	2	no	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	M₁₆×C₁₉	—	4	4	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	2	2	no	—
115	C₂×C₈×C₁₉	—	4	4	no	—
116	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₉	C₂²×C₄	1	4	yes	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	2	2	no	—
121	C₄⋊C₄×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	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	4	4	no	—
128	C₂²⋊C₄×C₁₉	—	4	4	no	—
129	C₂²⋊C₄×C₁₉	—	8	2	no	—
130	C₂²⋊C₄×C₁₉	—	8	2	no	—
131	C₂²⋊C₄×C₁₉	—	8	2	no	—
132	C₂²⋊C₄×C₁₉	—	8	2	no	—
133	C₄²×C₁₉	—	4	4	no	—
134	#21945	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	1	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
146	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
147	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₁₉	—	4	4	no	—
149	D₄×C₁₉	—	4	8	no	—
150	D₄×C₁₉	—	4	4	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	—	4	2	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	2	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	8	8	no	—
174	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
179	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
180	C₈×C₁₉	—	2	2	no	—
181	C₈×C₁₉	—	2	2	no	—
182	C₈×C₁₉	—	2	4	no	—
183	C₂×#408	C₂×C₁₉	1	1	yes	characteristic
184	#2311	C₂×C₁₉	1	2	yes	—
185	#1854	C₂×C₁₉	1	2	yes	complemented
186	#1854	C₂×C₁₉	1	2	yes	complemented
187	#1853	C₂×C₁₉	1	2	yes	complemented
188	#1852	C₂×C₁₉	1	2	yes	complemented
189	#1809	C₂×C₁₉	1	2	yes	complemented
190	#1808	C₂×C₁₉	1	1	yes	characteristic, complemented
191	#1807	C₂×C₁₉	1	1	yes	characteristic, complemented
192	C₂²×C₁₉	—	2	2	no	—
193	C₂²×C₁₉	—	2	4	no	—
194	C₂²×C₁₉	—	2	2	no	—
195	C₂²×C₁₉	—	2	4	no	—
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	4	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	—	4	2	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	2	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
205	C₂²×C₁₉	#534	1	2	yes	—
206	C₂²×C₁₉	#576	1	1	yes	characteristic
207	C₂²×C₁₉	#577	1	2	yes	—
208	C₂²×C₁₉	#578	1	1	yes	characteristic
209	C₄×C₁₉	—	2	4	no	—
210	C₄×C₁₉	—	2	2	no	—
211	C₄×C₁₉	—	8	2	no	—
212	C₄×C₁₉	—	8	2	no	—
213	C₄×C₁₉	—	8	2	no	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	#518	1	1	yes	characteristic
216	C₄×C₁₉	#518	1	1	yes	characteristic
217	C₄×C₁₉	#543	1	2	yes	—
218	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
219	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
220	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×#117	C₂²×C₁₉	1	2	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
223	C₂×#107	C₂²×C₁₉	1	2	yes	—
224	C₂×#107	C₂²×C₁₉	1	2	yes	—
225	C₂×#106	C₂²×C₁₉	1	2	yes	—
226	C₂×#106	C₂²×C₁₉	1	2	yes	—
227	#408	C₄×C₁₉	1	8	yes	complemented
228	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
230	#391	—	2	2	no	—
231	#390	—	2	2	no	—
232	#386	—	2	2	no	—
233	#386	—	2	2	no	—
234	#380	C₂²×C₁₉	1	2	yes	—
235	#380	C₂²×C₁₉	1	2	yes	—
236	#380	C₂²×C₁₉	1	2	yes	—
237	#380	C₂²×C₁₉	1	2	yes	—
238	#340	C₂²×C₁₉	1	1	yes	characteristic
239	#340	C₂²×C₁₉	1	1	yes	characteristic
240	#340	C₂²×C₁₉	1	1	yes	characteristic
241	#340	C₂²×C₁₉	1	1	yes	characteristic
242	#340	C₂²×C₁₉	1	2	yes	—
243	#340	C₂²×C₁₉	1	2	yes	—
244	C₂×C₁₉	—	4	4	no	—
245	C₂×C₁₉	—	4	2	no	—
246	C₂×C₁₉	#2315	1	1	yes	characteristic
247	C₂×C₁₉	#2912	1	1	yes	characteristic
248	C₂×C₁₉	#2913	1	1	yes	characteristic
249	C₂×C₁₉	#3198	1	2	yes	—
250	C₂×C₁₉	#3201	1	2	yes	—
251	C₂×#41	—	4	2	no	—
252	C₂×#41	—	4	2	no	—
253	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
254	C₂×#41	Q₈×C₁₉	1	4	yes	—
255	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
256	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
257	C₂²×D₄	D₄×C₁₉	1	2	yes	—
258	C₂³×C₄	—	2	2	no	—
259	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
261	C₂×M₁₆	—	4	2	no	—
262	C₂×M₁₆	C₂×C₄×C₁₉	1	4	yes	complemented
263	C₂²×C₈	—	4	2	no	—
264	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	complemented
265	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
268	#117	—	4	2	no	—
269	#117	—	4	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	4	2	no	—
272	C₂×C₄⋊C₄	—	4	2	no	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	2	no	—
283	#107	—	4	2	no	—
284	#107	—	4	2	no	—
285	#106	—	4	2	no	—
286	#106	—	4	2	no	—
287	C₂²⋊C₈	C₂×C₄×C₁₉	1	8	yes	complemented
288	C₂²⋊C₈	C₂×C₄×C₁₉	1	8	yes	complemented
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	C₁₉	#21945	1	1	yes	characteristic, direct product factor, Sylow
294	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
295	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
296	#41	—	4	4	no	—
297	#41	—	4	4	no	—
298	#41	—	4	8	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	C₄⋊C₄×C₁₉	1	4	yes	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	—
305	C₂×D₄	C₄⋊C₄×C₁₉	1	8	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	4	no	—
317	C₂²×C₄	—	8	2	no	—
318	C₂²×C₄	—	8	2	no	—
319	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
320	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
323	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
324	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
326	M₁₆	—	4	4	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	4	4	no	—
332	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
333	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
334	C₂×C₈	C₂²×C₄×C₁₉	1	4	yes	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	8	2	no	—
346	C₂²⋊C₄	—	8	2	no	—
347	C₂²⋊C₄	—	8	2	no	—
348	C₂²⋊C₄	—	8	2	no	—
349	C₄²	—	4	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	2	no	—
360	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
361	C₂³	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
362	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
363	Q₈	—	4	4	no	—
364	D₄	—	4	8	no	—
365	D₄	—	4	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	8	no	—
389	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
390	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	2	yes	—
391	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
393	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
394	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	4	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
411	C₂²	C₁₉×#534	1	2	yes	—
412	C₂²	C₁₉×#576	1	1	yes	characteristic
413	C₂²	C₁₉×#577	1	2	yes	—
414	C₂²	C₁₉×#578	1	1	yes	characteristic
415	C₄	—	2	4	no	—
416	C₄	—	2	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	2	no	—
421	C₄	C₁₉×#518	1	1	yes	characteristic
422	C₄	C₁₉×#518	1	1	yes	characteristic
423	C₄	C₁₉×#543	1	2	yes	—
424	C₂	—	4	4	no	—
425	C₂	—	4	2	no	—
426	C₂	C₁₉×#2315	1	1	yes	characteristic
427	C₂	C₁₉×#2912	1	1	yes	characteristic
428	C₂	C₁₉×#2913	1	1	yes	characteristic
429	C₂	C₁₉×#3198	1	2	yes	—
430	C₂	C₁₉×#3201	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₉×#1854	C₂	semidirect
4. C₁₉×#1854	C₂	semidirect
5. C₁₉×#1853	C₂	semidirect
6. C₁₉×#1852	C₂	semidirect
7. C₁₉×#1809	C₂	semidirect
8. C₁₉×#1808	C₂	semidirect
9. C₁₉×#1807	C₂	semidirect
19. C₁₉×#408	C₄	semidirect
47. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
49. C₂²×C₈×C₁₉	C₂×C₄	semidirect
72. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
73. C₁₉×C₂²⋊C₈	C₂×C₄	semidirect
134. #21945	C₁₉	direct (N × H)
185. #1854	C₂×C₁₉	semidirect
186. #1854	C₂×C₁₉	semidirect
187. #1853	C₂×C₁₉	semidirect
188. #1852	C₂×C₁₉	semidirect
189. #1809	C₂×C₁₉	semidirect
190. #1808	C₂×C₁₉	semidirect
191. #1807	C₂×C₁₉	semidirect
227. #408	C₄×C₁₉	semidirect
262. C₂×M₁₆	C₂×C₄×C₁₉	semidirect
264. C₂²×C₈	C₂×C₄×C₁₉	semidirect
287. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
288. C₂²⋊C₈	C₂×C₄×C₁₉	semidirect
293. C₁₉	#21945	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#408	2
C₁₉×#2311	2
C₁₉×#1854	2
C₁₉×#1853	2
C₁₉×#1852	2
C₁₉×#1809	2
C₁₉×#1808	2
C₁₉×#1807	2
#21945	19

Subgroups — C19×#21945 #18027904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#21945 #18027904