Subgroups — C₁₉×#16252 #18022211

Order 4864.

3514 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×#121	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₉×#392	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#392	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1439	C₂	1	4	yes	maximal, complemented
5	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
7	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
8	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#121	—	2	8	no	—
11	C₂×C₁₉×#121	—	2	16	no	—
12	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#392	—	2	16	no	—
17	C₁₉×#392	—	2	16	no	—
18	C₂×C₁₉×#95	C₂²	1	4	yes	—
19	C₂×C₁₉×#95	C₂²	1	4	yes	—
20	C₂⁵×C₁₉	C₂³	1	4	yes	—
21	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
22	C₂²×D₄×C₁₉	—	2	8	no	—
23	C₂²×D₄×C₁₉	—	2	8	no	—
24	C₂²×D₄×C₁₉	—	2	8	no	—
25	C₂²×D₄×C₁₉	—	2	16	no	—
26	C₂²×D₄×C₁₉	—	2	16	no	—
27	C₂²×D₄×C₁₉	—	2	8	no	—
28	C₂²×D₄×C₁₉	—	2	4	no	—
29	C₂²×D₄×C₁₉	—	2	8	no	—
30	C₂²×D₄×C₁₉	—	2	8	no	—
31	C₂²×D₄×C₁₉	—	4	4	no	—
32	C₂²×D₄×C₁₉	—	4	8	no	—
33	C₂²×D₄×C₁₉	—	4	8	no	—
34	C₂²×D₄×C₁₉	—	4	4	no	—
35	C₂²×D₄×C₁₉	—	4	4	no	—
36	C₂³×C₄×C₁₉	—	2	8	no	—
37	C₂³×C₄×C₁₉	—	4	2	no	—
38	C₂³×C₄×C₁₉	D₄	1	4	yes	complemented
39	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
40	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
42	C₁₉×#121	—	2	64	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
52	C₂×C₂²⋊C₄×C₁₉	D₄	1	16	yes	complemented
53	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	complemented
54	C₁₉×#95	—	2	8	no	—
55	C₁₉×#95	—	2	8	no	—
56	C₂⁴×C₁₉	—	2	4	no	—
57	C₂⁴×C₁₉	—	2	1	no	—
58	C₂⁴×C₁₉	—	2	2	no	—
59	C₂⁴×C₁₉	—	2	4	no	—
60	C₂⁴×C₁₉	—	2	1	no	—
61	C₂⁴×C₁₉	—	2	4	no	—
62	C₂⁴×C₁₉	—	2	4	no	—
63	C₂⁴×C₁₉	—	2	8	no	—
64	C₂⁴×C₁₉	—	2	8	no	—
65	C₂⁴×C₁₉	—	2	4	no	—
66	C₂⁴×C₁₉	—	2	4	no	—
67	C₂⁴×C₁₉	—	2	4	no	—
68	C₂⁴×C₁₉	—	2	8	no	—
69	C₂⁴×C₁₉	—	2	8	no	—
70	C₂⁴×C₁₉	—	2	4	no	—
71	C₂⁴×C₁₉	C₂×D₄	1	8	yes	—
72	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
73	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
74	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
75	C₂×D₄×C₁₉	—	2	16	no	—
76	C₂×D₄×C₁₉	—	2	32	no	—
77	C₂×D₄×C₁₉	—	4	32	no	—
78	C₂×D₄×C₁₉	—	4	32	no	—
79	C₂×D₄×C₁₉	—	4	32	no	—
80	C₂×D₄×C₁₉	—	4	8	no	—
81	C₂×D₄×C₁₉	—	4	16	no	—
82	C₂×D₄×C₁₉	—	4	32	no	—
83	C₂×D₄×C₁₉	—	4	16	no	—
84	C₂×D₄×C₁₉	—	4	16	no	—
85	C₂×D₄×C₁₉	—	4	32	no	—
86	C₂×D₄×C₁₉	—	4	16	no	—
87	C₂×D₄×C₁₉	—	4	16	no	—
88	C₂×D₄×C₁₉	—	4	8	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	4	no	—
93	C₂²×C₄×C₁₉	—	2	8	no	—
94	C₂²×C₄×C₁₉	—	2	8	no	—
95	C₂²×C₄×C₁₉	—	2	4	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	8	no	—
98	C₂²×C₄×C₁₉	—	2	8	no	—
99	C₂²×C₄×C₁₉	—	2	16	no	—
100	C₂²×C₄×C₁₉	—	4	4	no	—
101	C₂²×C₄×C₁₉	—	4	16	no	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
106	C₄⋊C₄×C₁₉	—	2	16	no	—
107	C₂²⋊C₄×C₁₉	—	2	32	no	—
108	C₂²⋊C₄×C₁₉	—	4	8	no	—
109	C₂²⋊C₄×C₁₉	—	4	32	no	—
110	#16252	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂³×C₁₉	—	2	4	no	—
112	C₂³×C₁₉	—	2	4	no	—
113	C₂³×C₁₉	—	2	2	no	—
114	C₂³×C₁₉	—	2	4	no	—
115	C₂³×C₁₉	—	2	2	no	—
116	C₂³×C₁₉	—	2	4	no	—
117	C₂³×C₁₉	—	2	16	no	—
118	C₂³×C₁₉	—	2	8	no	—
119	C₂³×C₁₉	—	2	8	no	—
120	C₂³×C₁₉	—	2	8	no	—
121	C₂³×C₁₉	—	2	16	no	—
122	C₂³×C₁₉	—	2	16	no	—
123	C₂³×C₁₉	—	4	4	no	—
124	C₂³×C₁₉	—	4	4	no	—
125	C₂³×C₁₉	—	4	4	no	—
126	C₂³×C₁₉	—	4	4	no	—
127	C₂³×C₁₉	—	4	4	no	—
128	C₂³×C₁₉	—	4	4	no	—
129	C₂³×C₁₉	—	4	4	no	—
130	C₂³×C₁₉	—	4	8	no	—
131	C₂³×C₁₉	—	4	8	no	—
132	C₂³×C₁₉	—	4	4	no	—
133	C₂³×C₁₉	—	4	4	no	—
134	C₂³×C₁₉	—	4	4	no	—
135	C₂³×C₁₉	—	4	4	no	—
136	C₂³×C₁₉	—	4	4	no	—
137	C₂³×C₁₉	—	4	8	no	—
138	C₂³×C₁₉	—	4	8	no	—
139	C₂³×C₁₉	—	4	8	no	—
140	C₂³×C₁₉	—	4	8	no	—
141	C₂³×C₁₉	—	4	8	no	—
142	C₂³×C₁₉	—	4	8	no	—
143	C₂³×C₁₉	—	4	8	no	—
144	C₂³×C₁₉	—	4	8	no	—
145	C₂³×C₁₉	#127	1	4	yes	—
146	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
147	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
148	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
149	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
150	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
151	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
152	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
153	D₄×C₁₉	—	4	32	no	—
154	D₄×C₁₉	—	4	64	no	—
155	D₄×C₁₉	—	4	64	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	16	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	16	no	—
162	C₂×C₄×C₁₉	—	2	16	no	—
163	C₂×C₄×C₁₉	—	4	16	no	—
164	C₂×C₄×C₁₉	—	4	4	no	—
165	C₂×C₄×C₁₉	—	4	8	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	8	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	#120	1	8	yes	—
171	C₂²×#121	C₂×C₁₉	1	2	yes	complemented
172	C₂×#392	C₂×C₁₉	1	4	yes	complemented
173	C₂×#392	C₂×C₁₉	1	4	yes	complemented
174	#1439	C₂×C₁₉	1	4	yes	complemented
175	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
176	C₂²×C₁₉	—	2	4	no	—
177	C₂²×C₁₉	—	2	8	no	—
178	C₂²×C₁₉	—	4	4	no	—
179	C₂²×C₁₉	—	4	2	no	—
180	C₂²×C₁₉	—	4	8	no	—
181	C₂²×C₁₉	—	4	8	no	—
182	C₂²×C₁₉	—	4	2	no	—
183	C₂²×C₁₉	—	4	8	no	—
184	C₂²×C₁₉	—	4	8	no	—
185	C₂²×C₁₉	—	4	16	no	—
186	C₂²×C₁₉	—	4	16	no	—
187	C₂²×C₁₉	—	4	8	no	—
188	C₂²×C₁₉	—	8	4	no	—
189	C₂²×C₁₉	—	8	4	no	—
190	C₂²×C₁₉	—	8	8	no	—
191	C₂²×C₁₉	—	8	8	no	—
192	C₂²×C₁₉	—	8	4	no	—
193	C₂²×C₁₉	—	8	4	no	—
194	C₂²×C₁₉	C₂×#120	1	2	yes	—
195	C₂²×C₁₉	C₂×#127	1	1	yes	characteristic
196	C₂²×C₁₉	#534	1	1	yes	characteristic
197	C₂²×C₁₉	#534	1	2	yes	—
198	C₂²×C₁₉	#535	1	4	yes	—
199	C₂²×C₁₉	#535	1	2	yes	—
200	C₂²×C₁₉	#537	1	1	yes	characteristic
201	C₂²×C₁₉	#537	1	4	yes	—
202	C₂²×C₁₉	#537	1	2	yes	—
203	C₂²×C₁₉	D₄²	1	4	yes	—
204	C₂²×C₁₉	D₄²	1	8	yes	—
205	C₂²×C₁₉	#560	1	4	yes	—
206	C₄×C₁₉	—	2	8	no	—
207	C₄×C₁₉	—	4	8	no	—
208	C₄×C₁₉	—	4	8	no	—
209	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
210	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
211	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
212	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
213	C₂×#121	—	2	8	no	—
214	C₂×#121	—	2	16	no	—
215	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
216	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
217	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
219	#392	—	2	16	no	—
220	#392	—	2	16	no	—
221	C₂×#95	C₂²×C₁₉	1	4	yes	—
222	C₂×#95	C₂²×C₁₉	1	4	yes	—
223	C₂×C₁₉	—	4	4	no	—
224	C₂×C₁₉	—	8	8	no	—
225	C₂×C₁₉	#2403	1	1	yes	characteristic
226	C₂×C₁₉	#2433	1	2	yes	—
227	C₂×C₁₉	#2615	1	2	yes	—
228	C₂×C₁₉	#2656	1	1	yes	characteristic
229	C₂×C₁₉	#2669	1	4	yes	—
230	C₂×C₁₉	#2675	1	4	yes	—
231	C₂×C₁₉	#2815	1	1	yes	characteristic
232	C₂⁵	C₂³×C₁₉	1	4	yes	—
233	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
234	C₂²×D₄	—	2	8	no	—
235	C₂²×D₄	—	2	8	no	—
236	C₂²×D₄	—	2	8	no	—
237	C₂²×D₄	—	2	16	no	—
238	C₂²×D₄	—	2	16	no	—
239	C₂²×D₄	—	2	8	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	8	no	—
242	C₂²×D₄	—	2	8	no	—
243	C₂²×D₄	—	4	4	no	—
244	C₂²×D₄	—	4	8	no	—
245	C₂²×D₄	—	4	8	no	—
246	C₂²×D₄	—	4	4	no	—
247	C₂²×D₄	—	4	4	no	—
248	C₂³×C₄	—	2	8	no	—
249	C₂³×C₄	—	4	2	no	—
250	C₂³×C₄	D₄×C₁₉	1	4	yes	complemented
251	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
252	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
253	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
254	#121	—	2	64	no	—
255	C₂×C₄⋊C₄	—	2	8	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₂²⋊C₄	—	2	8	no	—
258	C₂×C₂²⋊C₄	—	2	8	no	—
259	C₂×C₂²⋊C₄	—	2	16	no	—
260	C₂×C₂²⋊C₄	—	2	16	no	—
261	C₂×C₂²⋊C₄	—	4	2	no	—
262	C₂×C₂²⋊C₄	—	4	2	no	—
263	C₂×C₂²⋊C₄	—	4	8	no	—
264	C₂×C₂²⋊C₄	D₄×C₁₉	1	16	yes	complemented
265	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	complemented
266	#95	—	2	8	no	—
267	#95	—	2	8	no	—
268	C₁₉	#16252	1	1	yes	characteristic, direct product factor, Sylow
269	C₂⁴	—	2	4	no	—
270	C₂⁴	—	2	1	no	—
271	C₂⁴	—	2	2	no	—
272	C₂⁴	—	2	4	no	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	8	no	—
277	C₂⁴	—	2	8	no	—
278	C₂⁴	—	2	4	no	—
279	C₂⁴	—	2	4	no	—
280	C₂⁴	—	2	4	no	—
281	C₂⁴	—	2	8	no	—
282	C₂⁴	—	2	8	no	—
283	C₂⁴	—	2	4	no	—
284	C₂⁴	C₂×D₄×C₁₉	1	8	yes	—
285	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
286	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
287	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	32	no	—
290	C₂×D₄	—	4	32	no	—
291	C₂×D₄	—	4	32	no	—
292	C₂×D₄	—	4	32	no	—
293	C₂×D₄	—	4	8	no	—
294	C₂×D₄	—	4	16	no	—
295	C₂×D₄	—	4	32	no	—
296	C₂×D₄	—	4	16	no	—
297	C₂×D₄	—	4	16	no	—
298	C₂×D₄	—	4	32	no	—
299	C₂×D₄	—	4	16	no	—
300	C₂×D₄	—	4	16	no	—
301	C₂×D₄	—	4	8	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	16	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	—	4	16	no	—
315	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
316	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
317	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
318	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
319	C₄⋊C₄	—	2	16	no	—
320	C₂²⋊C₄	—	2	32	no	—
321	C₂²⋊C₄	—	4	8	no	—
322	C₂²⋊C₄	—	4	32	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	16	no	—
330	C₂³	—	2	8	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	2	8	no	—
333	C₂³	—	2	16	no	—
334	C₂³	—	2	16	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	—	4	8	no	—
343	C₂³	—	4	8	no	—
344	C₂³	—	4	4	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	8	no	—
348	C₂³	—	4	8	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	4	no	—
351	C₂³	—	4	8	no	—
352	C₂³	—	4	8	no	—
353	C₂³	—	4	8	no	—
354	C₂³	—	4	8	no	—
355	C₂³	—	4	8	no	—
356	C₂³	—	4	8	no	—
357	C₂³	C₁₉×#127	1	4	yes	—
358	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
359	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
360	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
361	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
363	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
364	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
365	D₄	—	4	32	no	—
366	D₄	—	4	64	no	—
367	D₄	—	4	64	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	16	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	16	no	—
374	C₂×C₄	—	2	16	no	—
375	C₂×C₄	—	4	16	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	C₁₉×#120	1	8	yes	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	8	no	—
391	C₂²	—	4	16	no	—
392	C₂²	—	4	16	no	—
393	C₂²	—	4	8	no	—
394	C₂²	—	4	8	no	—
395	C₂²	—	8	4	no	—
396	C₂²	—	8	8	no	—
397	C₂²	—	8	8	no	—
398	C₂²	—	8	4	no	—
399	C₂²	—	8	4	no	—
400	C₂²	—	8	4	no	—
401	C₂²	C₂×C₁₉×#120	1	2	yes	—
402	C₂²	C₂×C₁₉×#127	1	1	yes	characteristic
403	C₂²	C₁₉×#534	1	1	yes	characteristic
404	C₂²	C₁₉×#534	1	2	yes	—
405	C₂²	C₁₉×#535	1	4	yes	—
406	C₂²	C₁₉×#535	1	2	yes	—
407	C₂²	C₁₉×#537	1	2	yes	—
408	C₂²	C₁₉×#537	1	1	yes	characteristic
409	C₂²	C₁₉×#537	1	4	yes	—
410	C₂²	D₄²×C₁₉	1	4	yes	—
411	C₂²	D₄²×C₁₉	1	8	yes	—
412	C₂²	C₁₉×#560	1	4	yes	—
413	C₄	—	2	8	no	—
414	C₄	—	4	8	no	—
415	C₄	—	4	8	no	—
416	C₂	—	4	4	no	—
417	C₂	—	8	8	no	—
418	C₂	C₁₉×#2403	1	1	yes	characteristic
419	C₂	C₁₉×#2433	1	2	yes	—
420	C₂	C₁₉×#2615	1	2	yes	—
421	C₂	C₁₉×#2656	1	1	yes	characteristic
422	C₂	C₁₉×#2669	1	4	yes	—
423	C₂	C₁₉×#2675	1	4	yes	—
424	C₂	C₁₉×#2815	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×#121	C₂	semidirect
2. C₂×C₁₉×#392	C₂	semidirect
3. C₂×C₁₉×#392	C₂	semidirect
4. C₁₉×#1439	C₂	semidirect
5. C₁₉×C₂²⋊#95	C₂	semidirect
38. C₂³×C₄×C₁₉	D₄	semidirect
52. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
53. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
110. #16252	C₁₉	direct (N × H)
171. C₂²×#121	C₂×C₁₉	semidirect
172. C₂×#392	C₂×C₁₉	semidirect
173. C₂×#392	C₂×C₁₉	semidirect
174. #1439	C₂×C₁₉	semidirect
175. C₂²⋊#95	C₂×C₁₉	semidirect
250. C₂³×C₄	D₄×C₁₉	semidirect
264. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
265. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
268. C₁₉	#16252	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×#121	2
C₂×C₁₉×#392	2
C₁₉×#1439	2
C₁₉×C₂²⋊#95	2
#16252	19

Subgroups — C19×#16252 #18022211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#16252 #18022211