Subgroups — C₁₉×#32939 #18038898

Order 4864.

1494 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#469	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2615	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1895	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1893	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1809	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#131	—	2	8	no	—
12	C₂×C₁₉×#131	—	2	4	no	—
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
15	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
16	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	C₂²	1	4	yes	—
18	C₂×C₁₉×#121	C₂²	1	2	yes	—
19	C₁₉×#469	—	2	8	no	—
20	C₁₉×#466	—	2	4	no	—
21	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#106	C₂²	1	2	yes	—
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	4	yes	—
25	C₁₉×#393	—	2	2	no	—
26	C₁₉×#392	—	2	4	no	—
27	C₁₉×#392	—	2	2	no	—
28	C₁₉×#380	C₂²	1	4	yes	—
29	C₁₉×#380	C₂²	1	2	yes	—
30	C₁₉×#340	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	4	yes	—
32	C₂×#41×C₁₉	—	2	4	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	2	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₁₉	—	2	4	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₁₉	D₄	1	2	yes	—
41	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×D₈×C₁₉	—	2	2	no	—
45	C₂×D₈×C₁₉	—	2	4	no	—
46	C₁₉×#131	—	2	32	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	4	no	—
49	C₂×M₁₆×C₁₉	—	2	4	no	—
50	C₂×M₁₆×C₁₉	—	2	4	no	—
51	C₂×M₁₆×C₁₉	D₄	1	8	yes	complemented
52	C₂²×C₈×C₁₉	—	2	4	no	—
53	C₂²×C₈×C₁₉	—	2	4	no	—
54	C₂²×C₈×C₁₉	—	2	4	no	—
55	C₂²×C₈×C₁₉	—	2	4	no	—
56	C₂²×C₈×C₁₉	D₄	1	4	yes	complemented
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₁₉×#121	—	2	4	no	—
61	C₁₉×#121	—	2	8	no	—
62	C₁₉×#121	—	2	8	no	—
63	C₁₉×#121	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₁₉×#107	—	2	2	no	—
71	C₁₉×#106	—	2	4	no	—
72	C₁₉×#102	—	2	4	no	—
73	C₁₉×#102	—	2	8	no	—
74	C₁₉×#95	—	2	4	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
78	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
79	#41×C₁₉	—	2	8	no	—
80	#41×C₁₉	—	2	16	no	—
81	#41×C₁₉	—	2	8	no	—
82	C₂×Q₈×C₁₉	—	2	2	no	—
83	C₂×Q₈×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	2	no	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	2	2	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	4	4	no	—
94	C₂×D₄×C₁₉	—	4	8	no	—
95	C₂×D₄×C₁₉	—	8	4	no	—
96	C₂×D₄×C₁₉	—	8	4	no	—
97	C₂×D₄×C₁₉	—	8	4	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	#41	1	2	yes	—
111	C₂²×C₄×C₁₉	#41	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	D₈×C₁₉	—	4	4	no	—
114	M₁₆×C₁₉	—	2	8	no	—
115	M₁₆×C₁₉	—	2	16	no	—
116	C₂×C₈×C₁₉	—	2	16	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	8	no	—
121	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
123	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
124	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₁₉	—	2	4	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₂²⋊C₄×C₁₉	—	4	4	no	—
130	C₂²⋊C₄×C₁₉	—	4	8	no	—
131	C₂²⋊C₄×C₁₉	—	8	4	no	—
132	C₂²⋊C₄×C₁₉	—	8	2	no	—
133	#32939	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	2	2	no	—
135	C₂³×C₁₉	—	2	2	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	4	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	2	4	no	—
141	C₂³×C₁₉	—	4	2	no	—
142	C₂³×C₁₉	—	4	4	no	—
143	C₂³×C₁₉	—	4	4	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	#121	1	2	yes	—
147	C₂³×C₁₉	#121	1	4	yes	—
148	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₁₉	—	2	8	no	—
150	D₄×C₁₉	—	2	16	no	—
151	D₄×C₁₉	—	2	8	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	4	2	no	—
154	D₄×C₁₉	—	4	4	no	—
155	D₄×C₁₉	—	8	8	no	—
156	D₄×C₁₉	—	8	16	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	4	no	—
172	C₂×C₄×C₁₉	#121	1	2	yes	—
173	C₂×C₄×C₁₉	#121	1	4	yes	—
174	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
178	C₈×C₁₉	—	2	2	no	—
179	C₈×C₁₉	—	2	4	no	—
180	C₈×C₁₉	#120	1	4	yes	—
181	C₂²×#131	C₂×C₁₉	1	1	yes	characteristic, complemented
182	C₂×#469	C₂×C₁₉	1	2	yes	complemented
183	C₂×#466	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#2615	C₂×C₁₉	1	2	yes	complemented
185	#1895	C₂×C₁₉	1	2	yes	complemented
186	#1893	C₂×C₁₉	1	4	yes	complemented
187	#1809	C₂×C₁₉	1	2	yes	complemented
188	#1807	C₂×C₁₉	1	1	yes	characteristic, complemented
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	4	no	—
191	C₂²×C₁₉	—	2	2	no	—
192	C₂²×C₁₉	—	2	2	no	—
193	C₂²×C₁₉	—	2	8	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	4	no	—
197	C₂²×C₁₉	—	4	4	no	—
198	C₂²×C₁₉	—	8	2	no	—
199	C₂²×C₁₉	—	8	2	no	—
200	C₂²×C₁₉	—	8	2	no	—
201	C₂²×C₁₉	—	8	4	no	—
202	C₂²×C₁₉	—	8	4	no	—
203	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
204	C₂²×C₁₉	C₂×#121	1	2	yes	—
205	C₂²×C₁₉	#576	1	2	yes	—
206	C₂²×C₁₉	#577	1	2	yes	—
207	C₄×C₁₉	—	2	4	no	—
208	C₄×C₁₉	—	2	2	no	—
209	C₄×C₁₉	—	8	2	no	—
210	C₄×C₁₉	—	8	4	no	—
211	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
212	C₄×C₁₉	#525	1	2	yes	—
213	C₄×C₁₉	#525	1	1	yes	characteristic
214	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
215	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
216	C₂×#131	—	2	8	no	—
217	C₂×#131	—	2	4	no	—
218	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
219	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
220	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
221	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
222	C₂×#121	C₂²×C₁₉	1	4	yes	—
223	C₂×#121	C₂²×C₁₉	1	2	yes	—
224	#469	—	2	8	no	—
225	#466	—	2	4	no	—
226	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×#106	C₂²×C₁₉	1	2	yes	—
228	C₂×#102	C₂²×C₁₉	1	2	yes	—
229	C₂×#102	C₂²×C₁₉	1	4	yes	—
230	#393	—	2	2	no	—
231	#392	—	2	2	no	—
232	#392	—	2	4	no	—
233	#380	C₂²×C₁₉	1	2	yes	—
234	#380	C₂²×C₁₉	1	4	yes	—
235	#340	C₂²×C₁₉	1	2	yes	—
236	#340	C₂²×C₁₉	1	4	yes	—
237	C₂×C₁₉	—	4	2	no	—
238	C₂×C₁₉	—	4	4	no	—
239	C₂×C₁₉	—	16	2	no	—
240	C₂×C₁₉	#2847	1	1	yes	characteristic
241	C₂×C₁₉	#3058	1	1	yes	characteristic
242	C₂×C₁₉	#3060	1	1	yes	characteristic
243	C₂×C₁₉	#3062	1	4	yes	—
244	C₂×#41	—	2	4	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	4	no	—
248	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
249	C₂²×D₄	—	2	4	no	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
252	C₂²×D₄	D₄×C₁₉	1	2	yes	—
253	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
254	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	—	2	4	no	—
258	#131	—	2	32	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	4	no	—
261	C₂×M₁₆	—	2	4	no	—
262	C₂×M₁₆	—	2	4	no	—
263	C₂×M₁₆	D₄×C₁₉	1	8	yes	complemented
264	C₂²×C₈	—	2	4	no	—
265	C₂²×C₈	—	2	4	no	—
266	C₂²×C₈	—	2	4	no	—
267	C₂²×C₈	—	2	4	no	—
268	C₂²×C₈	D₄×C₁₉	1	4	yes	complemented
269	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
271	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
272	#121	—	2	4	no	—
273	#121	—	2	8	no	—
274	#121	—	2	8	no	—
275	#121	—	2	4	no	—
276	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	4	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	#107	—	2	2	no	—
283	#106	—	2	4	no	—
284	#102	—	2	4	no	—
285	#102	—	2	8	no	—
286	#95	—	2	2	no	—
287	#95	—	2	4	no	—
288	C₁₉	#32939	1	1	yes	characteristic, direct product factor, Sylow
289	C₂⁴	—	2	2	no	—
290	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
291	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
292	#41	—	2	8	no	—
293	#41	—	2	16	no	—
294	#41	—	2	8	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	4	4	no	—
307	C₂×D₄	—	4	8	no	—
308	C₂×D₄	—	8	4	no	—
309	C₂×D₄	—	8	4	no	—
310	C₂×D₄	—	8	4	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	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
322	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
323	C₂²×C₄	#41×C₁₉	1	2	yes	—
324	C₂²×C₄	#41×C₁₉	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
326	D₈	—	4	4	no	—
327	M₁₆	—	2	8	no	—
328	M₁₆	—	2	16	no	—
329	C₂×C₈	—	2	16	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	8	no	—
334	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
335	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
336	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
337	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	8	no	—
344	C₂²⋊C₄	—	8	4	no	—
345	C₂²⋊C₄	—	8	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	C₁₉×#121	1	2	yes	—
359	C₂³	C₁₉×#121	1	4	yes	—
360	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
361	Q₈	—	2	8	no	—
362	D₄	—	2	16	no	—
363	D₄	—	2	8	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	4	no	—
367	D₄	—	8	8	no	—
368	D₄	—	8	16	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	C₁₉×#121	1	2	yes	—
385	C₂×C₄	C₁₉×#121	1	4	yes	—
386	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
388	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
390	C₈	—	2	2	no	—
391	C₈	—	2	4	no	—
392	C₈	C₁₉×#120	1	4	yes	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	8	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	4	no	—
405	C₂²	—	8	4	no	—
406	C₂²	—	8	2	no	—
407	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
408	C₂²	C₂×C₁₉×#121	1	2	yes	—
409	C₂²	C₁₉×#576	1	2	yes	—
410	C₂²	C₁₉×#577	1	2	yes	—
411	C₄	—	2	4	no	—
412	C₄	—	2	2	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	4	no	—
415	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
416	C₄	C₁₉×#525	1	2	yes	—
417	C₄	C₁₉×#525	1	1	yes	characteristic
418	C₂	—	4	2	no	—
419	C₂	—	4	4	no	—
420	C₂	—	16	2	no	—
421	C₂	C₁₉×#2847	1	1	yes	characteristic
422	C₂	C₁₉×#3058	1	1	yes	characteristic
423	C₂	C₁₉×#3060	1	1	yes	characteristic
424	C₂	C₁₉×#3062	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×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
1. C₂²×C₁₉×#131	C₂	semidirect
2. C₂×C₁₉×#469	C₂	semidirect
3. C₂×C₁₉×#466	C₂	semidirect
4. C₁₉×#2615	C₂	semidirect
5. C₁₉×#1895	C₂	semidirect
6. C₁₉×#1893	C₂	semidirect
7. C₁₉×#1809	C₂	semidirect
8. C₁₉×#1807	C₂	semidirect
51. C₂×M₁₆×C₁₉	D₄	semidirect
56. C₂²×C₈×C₁₉	D₄	semidirect
133. #32939	C₁₉	direct (N × H)
181. C₂²×#131	C₂×C₁₉	semidirect
182. C₂×#469	C₂×C₁₉	semidirect
183. C₂×#466	C₂×C₁₉	semidirect
184. #2615	C₂×C₁₉	semidirect
185. #1895	C₂×C₁₉	semidirect
186. #1893	C₂×C₁₉	semidirect
187. #1809	C₂×C₁₉	semidirect
188. #1807	C₂×C₁₉	semidirect
263. C₂×M₁₆	D₄×C₁₉	semidirect
268. C₂²×C₈	D₄×C₁₉	semidirect
288. C₁₉	#32939	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#131	2
C₂×C₁₉×#469	2
C₂×C₁₉×#466	2
C₁₉×#2615	2
C₁₉×#1895	2
C₁₉×#1893	2
C₁₉×#1809	2
C₁₉×#1807	2
#32939	19

Subgroups — C19×#32939 #18038898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32939 #18038898