Subgroups — C₁₉×#32782 #18038741

Order 4864.

744 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2619	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2094	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2085	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2041	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2034	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#107	C₂²	1	2	yes	—
18	C₂×C₁₉×#106	C₂²	1	2	yes	—
19	C₂×C₁₉×#102	C₂²	1	2	yes	—
20	C₂×C₁₉×#102	C₂²	1	2	yes	—
21	C₂×C₁₉×#102	C₂²	1	2	yes	—
22	C₂×C₁₉×#102	C₂²	1	2	yes	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₁₉×#398	—	2	2	no	—
25	C₁₉×#396	—	2	2	no	—
26	C₁₉×#394	—	2	2	no	—
27	C₁₉×#392	—	2	2	no	—
28	C₁₉×#390	C₂²	1	1	yes	characteristic
29	C₁₉×#390	C₂²	1	1	yes	characteristic
30	C₁₉×#389	C₂²	1	2	yes	—
31	C₁₉×#384	C₂²	1	1	yes	characteristic
32	C₁₉×#382	C₂²	1	1	yes	characteristic
33	C₁₉×#380	C₂²	1	2	yes	—
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#336	C₂²	1	1	yes	characteristic
37	C₁₉×#336	C₂²	1	1	yes	characteristic
38	C₁₉×#336	C₂²	1	2	yes	—
39	C₂²×D₄×C₁₉	—	2	1	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	2	no	—
42	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
47	C₁₉×#127	—	4	2	no	—
48	C₁₉×#125	—	4	2	no	—
49	C₁₉×#121	—	4	2	no	—
50	C₁₉×#121	—	4	2	no	—
51	C₁₉×#117	—	4	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	2	yes	—
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×#107	—	4	2	no	—
69	C₁₉×#106	—	4	2	no	—
70	C₁₉×#102	—	4	2	no	—
71	C₁₉×#102	—	4	2	no	—
72	C₁₉×#102	—	4	2	no	—
73	C₁₉×#102	—	4	2	no	—
74	C₁₉×C₂²⋊C₈	—	4	2	no	—
75	C₁₉×#95	—	2	2	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	1	no	—
79	C₂⁴×C₁₉	—	2	1	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×D₄×C₁₉	—	2	2	no	—
82	C₂×D₄×C₁₉	—	2	2	no	—
83	C₂×D₄×C₁₉	—	2	2	no	—
84	C₂×D₄×C₁₉	—	2	2	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	2	1	no	—
87	C₂×D₄×C₁₉	—	2	1	no	—
88	C₂×D₄×C₁₉	—	2	1	no	—
89	C₂×D₄×C₁₉	—	4	4	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	8	2	no	—
93	C₂×D₄×C₁₉	—	8	2	no	—
94	C₂×D₄×C₁₉	—	8	2	no	—
95	C₂×D₄×C₁₉	—	8	2	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	2	2	no	—
98	C₂²×C₄×C₁₉	—	2	1	no	—
99	C₂²×C₄×C₁₉	—	2	1	no	—
100	C₂²×C₄×C₁₉	—	2	1	no	—
101	C₂²×C₄×C₁₉	—	2	1	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	2	2	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	4	2	no	—
121	C₄⋊C₄×C₁₉	—	4	4	no	—
122	C₄⋊C₄×C₁₉	—	8	2	no	—
123	C₄⋊C₄×C₁₉	—	8	2	no	—
124	C₂²⋊C₄×C₁₉	—	4	2	no	—
125	C₂²⋊C₄×C₁₉	—	4	2	no	—
126	C₂²⋊C₄×C₁₉	—	4	2	no	—
127	C₂²⋊C₄×C₁₉	—	8	2	no	—
128	C₂²⋊C₄×C₁₉	—	8	2	no	—
129	C₂²⋊C₄×C₁₉	—	8	2	no	—
130	C₄²×C₁₉	—	2	2	no	—
131	C₄²×C₁₉	—	2	2	no	—
132	#32782	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₁₉	—	2	1	no	—
134	C₂³×C₁₉	—	2	1	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	4	1	no	—
139	C₂³×C₁₉	—	4	1	no	—
140	C₂³×C₁₉	—	4	1	no	—
141	C₂³×C₁₉	—	4	1	no	—
142	C₂³×C₁₉	—	4	1	no	—
143	C₂³×C₁₉	—	4	1	no	—
144	C₂³×C₁₉	—	4	2	no	—
145	C₂³×C₁₉	—	4	2	no	—
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	—	4	2	no	—
148	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
149	D₄×C₁₉	—	4	2	no	—
150	D₄×C₁₉	—	4	2	no	—
151	D₄×C₁₉	—	4	2	no	—
152	D₄×C₁₉	—	4	2	no	—
153	D₄×C₁₉	—	8	8	no	—
154	D₄×C₁₉	—	8	4	no	—
155	D₄×C₁₉	—	8	4	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	1	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	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	1	no	—
169	C₂×C₄×C₁₉	—	4	1	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	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
178	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
179	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
181	C₈×C₁₉	—	4	2	no	—
182	C₈×C₁₉	—	4	2	no	—
183	#2629	C₂×C₁₉	1	1	yes	characteristic, complemented
184	#2619	C₂×C₁₉	1	1	yes	characteristic
185	#2094	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#2093	C₂×C₁₉	1	1	yes	characteristic, complemented
187	#2085	C₂×C₁₉	1	2	yes	complemented
188	#2041	C₂×C₁₉	1	2	yes	complemented
189	#2034	C₂×C₁₉	1	2	yes	complemented
190	#2033	C₂×C₁₉	1	2	yes	complemented
191	#2025	C₂×C₁₉	1	1	yes	characteristic, complemented
192	#2025	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#1818	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂²×C₁₉	—	4	1	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	4	1	no	—
197	C₂²×C₁₉	—	4	1	no	—
198	C₂²×C₁₉	—	4	2	no	—
199	C₂²×C₁₉	—	8	1	no	—
200	C₂²×C₁₉	—	8	1	no	—
201	C₂²×C₁₉	—	8	2	no	—
202	C₂²×C₁₉	—	8	2	no	—
203	C₂²×C₁₉	—	8	1	no	—
204	C₂²×C₁₉	—	8	1	no	—
205	C₂²×C₁₉	—	8	1	no	—
206	C₂²×C₁₉	—	8	1	no	—
207	C₂²×C₁₉	—	8	2	no	—
208	C₂²×C₁₉	—	8	2	no	—
209	C₂²×C₁₉	#534	1	1	yes	characteristic
210	C₂²×C₁₉	#535	1	1	yes	characteristic
211	C₂²×C₁₉	#536	1	1	yes	characteristic
212	C₂²×C₁₉	#576	1	2	yes	—
213	C₂²×C₁₉	#577	1	2	yes	—
214	C₄×C₁₉	—	4	1	no	—
215	C₄×C₁₉	—	4	2	no	—
216	C₄×C₁₉	—	4	2	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	—	8	2	no	—
219	C₄×C₁₉	—	8	1	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	#562	1	2	yes	—
222	C₄×C₁₉	#562	1	2	yes	—
223	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
225	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
226	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#107	C₂²×C₁₉	1	2	yes	—
229	C₂×#106	C₂²×C₁₉	1	2	yes	—
230	C₂×#102	C₂²×C₁₉	1	2	yes	—
231	C₂×#102	C₂²×C₁₉	1	2	yes	—
232	C₂×#102	C₂²×C₁₉	1	2	yes	—
233	C₂×#102	C₂²×C₁₉	1	2	yes	—
234	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
235	#398	—	2	2	no	—
236	#396	—	2	2	no	—
237	#394	—	2	2	no	—
238	#392	—	2	2	no	—
239	#390	C₂²×C₁₉	1	1	yes	characteristic
240	#390	C₂²×C₁₉	1	1	yes	characteristic
241	#389	C₂²×C₁₉	1	2	yes	—
242	#384	C₂²×C₁₉	1	1	yes	characteristic
243	#382	C₂²×C₁₉	1	1	yes	characteristic
244	#380	C₂²×C₁₉	1	2	yes	—
245	#340	C₂²×C₁₉	1	2	yes	—
246	#340	C₂²×C₁₉	1	2	yes	—
247	#336	C₂²×C₁₉	1	2	yes	—
248	#336	C₂²×C₁₉	1	1	yes	characteristic
249	#336	C₂²×C₁₉	1	1	yes	characteristic
250	C₂×C₁₉	—	8	1	no	—
251	C₂×C₁₉	—	16	1	no	—
252	C₂×C₁₉	—	16	1	no	—
253	C₂×C₁₉	#2816	1	1	yes	characteristic
254	C₂×C₁₉	#3198	1	2	yes	—
255	C₂×C₁₉	#3220	1	1	yes	characteristic
256	C₂×C₁₉	#3222	1	1	yes	characteristic
257	C₂×C₁₉	#3241	1	2	yes	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
262	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
266	#127	—	4	2	no	—
267	#125	—	4	2	no	—
268	#121	—	4	2	no	—
269	#121	—	4	2	no	—
270	#117	—	4	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
285	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
287	#107	—	4	2	no	—
288	#106	—	4	2	no	—
289	#102	—	4	2	no	—
290	#102	—	4	2	no	—
291	#102	—	4	2	no	—
292	#102	—	4	2	no	—
293	C₂²⋊C₈	—	4	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	C₁₉	#32782	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁴	—	2	1	no	—
299	C₂⁴	—	2	1	no	—
300	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	8	2	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	—	8	2	no	—
315	C₂×D₄	—	8	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
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	—	4	2	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₄⋊C₄	—	8	2	no	—
343	C₄⋊C₄	—	8	2	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	8	2	no	—
348	C₂²⋊C₄	—	8	2	no	—
349	C₂²⋊C₄	—	8	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	4	1	no	—
358	C₂³	—	4	1	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
368	D₄	—	4	2	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	8	no	—
373	D₄	—	8	4	no	—
374	D₄	—	8	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
397	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
398	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
399	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	2	no	—
414	C₂²	—	8	2	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	C₁₉×#534	1	1	yes	characteristic
418	C₂²	C₁₉×#535	1	1	yes	characteristic
419	C₂²	C₁₉×#536	1	1	yes	characteristic
420	C₂²	C₁₉×#576	1	2	yes	—
421	C₂²	C₁₉×#577	1	2	yes	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	1	no	—
429	C₄	C₁₉×#562	1	2	yes	—
430	C₄	C₁₉×#562	1	2	yes	—
431	C₂	—	8	1	no	—
432	C₂	—	16	1	no	—
433	C₂	—	16	1	no	—
434	C₂	C₁₉×#2816	1	1	yes	characteristic
435	C₂	C₁₉×#3198	1	2	yes	—
436	C₂	C₁₉×#3220	1	1	yes	characteristic
437	C₂	C₁₉×#3222	1	1	yes	characteristic
438	C₂	C₁₉×#3241	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2619	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2629	C₂	semidirect
3. C₁₉×#2094	C₂	semidirect
4. C₁₉×#2093	C₂	semidirect
5. C₁₉×#2085	C₂	semidirect
6. C₁₉×#2041	C₂	semidirect
7. C₁₉×#2034	C₂	semidirect
8. C₁₉×#2033	C₂	semidirect
9. C₁₉×#2025	C₂	semidirect
10. C₁₉×#2025	C₂	semidirect
11. C₁₉×#1818	C₂	semidirect
132. #32782	C₁₉	direct (N × H)
183. #2629	C₂×C₁₉	semidirect
185. #2094	C₂×C₁₉	semidirect
186. #2093	C₂×C₁₉	semidirect
187. #2085	C₂×C₁₉	semidirect
188. #2041	C₂×C₁₉	semidirect
189. #2034	C₂×C₁₉	semidirect
190. #2033	C₂×C₁₉	semidirect
191. #2025	C₂×C₁₉	semidirect
192. #2025	C₂×C₁₉	semidirect
193. #1818	C₂×C₁₉	semidirect
297. C₁₉	#32782	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×#2629	2
C₁₉×#2619	2
C₁₉×#2094	2
C₁₉×#2093	2
C₁₉×#2085	2
C₁₉×#2041	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#2025	2
C₁₉×#1818	2
#32782	19

Subgroups — C19×#32782 #18038741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32782 #18038741