Subgroups — C₁₉×#23137 #18029096

Order 4864.

966 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#466	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2363	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1936	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1918	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1879	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1875	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1762	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#121	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
14	C₂×C₁₉×#117	C₂²	1	2	yes	—
15	C₁₉×#466	C₄	1	8	yes	complemented
16	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#102	C₂²	1	2	yes	—
18	C₂×C₁₉×#102	C₂²	1	2	yes	—
19	C₂×C₁₉×#102	C₂²	1	2	yes	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#97	C₂²	1	2	yes	—
22	C₁₉×#390	—	2	2	no	—
23	C₁₉×#390	C₂²	1	2	yes	—
24	C₁₉×#389	C₂²	1	2	yes	—
25	C₁₉×#388	—	2	2	no	—
26	C₁₉×#386	—	2	2	no	—
27	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₁₉	—	2	2	no	—
29	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#340	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	2	yes	—
33	C₁₉×#340	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	1	yes	characteristic
35	C₁₉×#336	C₂²	1	2	yes	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₉	—	2	2	no	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×D₈×C₁₉	—	4	2	no	—
41	C₂×D₈×C₁₉	C₂×C₄	1	4	yes	—
42	C₂²×C₈×C₁₉	—	4	2	no	—
43	C₂²×C₈×C₁₉	C₂×C₄	1	4	yes	complemented
44	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
47	C₁₉×#121	—	2	4	no	—
48	C₁₉×#121	C₂×C₄	1	8	yes	complemented
49	C₄×D₄×C₁₉	—	2	4	no	—
50	C₄×D₄×C₁₉	—	4	2	no	—
51	C₁₉×#117	—	2	4	no	—
52	C₁₉×#117	—	4	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₉	—	2	2	no	—
65	C₂×C₄²×C₁₉	—	2	2	no	—
66	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
67	C₁₉×#107	C₂×C₄	1	4	yes	complemented
68	C₁₉×#102	—	2	4	no	—
69	C₁₉×#102	—	4	2	no	—
70	C₁₉×#102	C₂×C₄	1	8	yes	complemented
71	C₁₉×C₂²⋊C₈	—	2	2	no	—
72	C₁₉×#97	—	4	2	no	—
73	C₁₉×#95	—	2	2	no	—
74	C₁₉×#95	—	2	2	no	—
75	C₁₉×#95	D₄	1	2	yes	—
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂×D₄×C₁₉	—	2	8	no	—
79	C₂×D₄×C₁₉	—	2	2	no	—
80	C₂×D₄×C₁₉	—	2	2	no	—
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	—	8	2	no	—
85	C₂×D₄×C₁₉	—	8	2	no	—
86	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	4	4	no	—
93	C₂²×C₄×C₁₉	—	4	4	no	—
94	C₂²×C₄×C₁₉	—	8	2	no	—
95	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	2	yes	—
100	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
101	D₈×C₁₉	—	4	4	no	—
102	C₂×C₈×C₁₉	—	2	2	no	—
103	C₂×C₈×C₁₉	—	2	2	no	—
104	C₂×C₈×C₁₉	—	2	2	no	—
105	C₂×C₈×C₁₉	—	2	2	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	4	4	no	—
108	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₁₉	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₁₉	—	2	2	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	2	no	—
114	C₄⋊C₄×C₁₉	—	8	2	no	—
115	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
116	C₄⋊C₄×C₁₉	#41	1	4	yes	—
117	C₂²⋊C₄×C₁₉	—	2	8	no	—
118	C₂²⋊C₄×C₁₉	—	4	1	no	—
119	C₂²⋊C₄×C₁₉	—	4	1	no	—
120	C₂²⋊C₄×C₁₉	—	4	4	no	—
121	C₂²⋊C₄×C₁₉	—	4	4	no	—
122	C₂²⋊C₄×C₁₉	—	4	4	no	—
123	C₂²⋊C₄×C₁₉	—	8	2	no	—
124	C₄²×C₁₉	—	2	2	no	—
125	C₄²×C₁₉	—	2	2	no	—
126	C₄²×C₁₉	—	4	4	no	—
127	C₄²×C₁₉	—	8	2	no	—
128	#23137	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₁₉	—	2	2	no	—
130	C₂³×C₁₉	—	2	1	no	—
131	C₂³×C₁₉	—	2	1	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	4	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	2	no	—
137	C₂³×C₁₉	—	4	2	no	—
138	C₂³×C₁₉	—	4	2	no	—
139	C₂³×C₁₉	—	4	2	no	—
140	C₂³×C₁₉	C₄×D₄	1	2	yes	—
141	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
142	D₄×C₁₉	—	2	4	no	—
143	D₄×C₁₉	—	2	4	no	—
144	D₄×C₁₉	—	4	2	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	—	8	8	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	4	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	2	2	no	—
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	2	no	—
157	C₂×C₄×C₁₉	—	2	2	no	—
158	C₂×C₄×C₁₉	—	2	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	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	—	8	8	no	—
167	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
170	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
172	C₈×C₁₉	—	2	2	no	—
173	C₈×C₁₉	—	2	2	no	—
174	C₈×C₁₉	—	4	2	no	—
175	C₂×#466	C₂×C₁₉	1	1	yes	characteristic
176	#2363	C₂×C₁₉	1	2	yes	complemented
177	#1936	C₂×C₁₉	1	2	yes	complemented
178	#1918	C₂×C₁₉	1	2	yes	complemented
179	#1879	C₂×C₁₉	1	2	yes	complemented
180	#1875	C₂×C₁₉	1	2	yes	complemented
181	#1762	C₂×C₁₉	1	2	yes	complemented
182	#1752	C₂×C₁₉	1	1	yes	characteristic, complemented
183	#1735	C₂×C₁₉	1	1	yes	characteristic, complemented
184	C₂²×C₁₉	—	2	2	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	2	no	—
187	C₂²×C₁₉	—	4	2	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	4	4	no	—
190	C₂²×C₁₉	—	4	4	no	—
191	C₂²×C₁₉	—	4	4	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	—	8	2	no	—
195	C₂²×C₁₉	—	8	2	no	—
196	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₁₉	#546	1	2	yes	—
198	C₂²×C₁₉	#575	1	1	yes	characteristic
199	C₂²×C₁₉	#575	1	1	yes	characteristic
200	C₂²×C₁₉	#576	1	2	yes	—
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	4	4	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	4	2	no	—
205	C₄×C₁₉	—	4	4	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₄×C₁₉	C₄×#41	1	1	yes	characteristic
208	C₄×C₁₉	#518	1	1	yes	characteristic
209	C₄×C₁₉	#553	1	2	yes	—
210	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
212	C₂×#121	C₂²×C₁₉	1	2	yes	—
213	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
214	C₂×#117	C₂²×C₁₉	1	2	yes	—
215	#466	C₄×C₁₉	1	8	yes	complemented
216	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
217	C₂×#102	C₂²×C₁₉	1	2	yes	—
218	C₂×#102	C₂²×C₁₉	1	2	yes	—
219	C₂×#102	C₂²×C₁₉	1	2	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
221	C₂×#97	C₂²×C₁₉	1	2	yes	—
222	#390	—	2	2	no	—
223	#390	C₂²×C₁₉	1	2	yes	—
224	#389	C₂²×C₁₉	1	2	yes	—
225	#388	—	2	2	no	—
226	#386	—	2	2	no	—
227	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
228	C₄×C₂²⋊C₄	—	2	2	no	—
229	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
230	#340	C₂²×C₁₉	1	2	yes	—
231	#340	C₂²×C₁₉	1	2	yes	—
232	#340	C₂²×C₁₉	1	2	yes	—
233	#340	C₂²×C₁₉	1	1	yes	characteristic
234	#340	C₂²×C₁₉	1	1	yes	characteristic
235	#336	C₂²×C₁₉	1	2	yes	—
236	C₂×C₁₉	—	4	2	no	—
237	C₂×C₁₉	—	8	4	no	—
238	C₂×C₁₉	#2364	1	1	yes	characteristic
239	C₂×C₁₉	#2943	1	1	yes	characteristic
240	C₂×C₁₉	#2948	1	1	yes	characteristic
241	C₂×C₁₉	#3309	1	2	yes	—
242	C₂×C₁₉	#3319	1	2	yes	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂×D₈	—	4	2	no	—
248	C₂×D₈	C₂×C₄×C₁₉	1	4	yes	—
249	C₂²×C₈	—	4	2	no	—
250	C₂²×C₈	C₂×C₄×C₁₉	1	4	yes	complemented
251	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
254	#121	—	2	4	no	—
255	#121	C₂×C₄×C₁₉	1	8	yes	complemented
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	4	2	no	—
258	#117	—	2	4	no	—
259	#117	—	4	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
274	#107	C₂×C₄×C₁₉	1	4	yes	complemented
275	#102	—	2	4	no	—
276	#102	—	4	2	no	—
277	#102	C₂×C₄×C₁₉	1	8	yes	complemented
278	C₂²⋊C₈	—	2	2	no	—
279	#97	—	4	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	D₄×C₁₉	1	2	yes	—
283	C₁₉	#23137	1	1	yes	characteristic, direct product factor, Sylow
284	C₂⁴	—	2	2	no	—
285	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	8	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
307	C₂²×C₄	#41×C₁₉	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
309	D₈	—	4	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
317	C₂×C₈	C₂²×C₄×C₁₉	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	8	2	no	—
323	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
324	C₄⋊C₄	#41×C₁₉	1	4	yes	—
325	C₂²⋊C₄	—	2	8	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	4	4	no	—
335	C₄²	—	8	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	C₄×D₄×C₁₉	1	2	yes	—
348	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
349	D₄	—	2	4	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	8	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	8	no	—
374	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
375	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
377	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
378	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
395	C₂²	C₁₉×#546	1	2	yes	—
396	C₂²	C₁₉×#575	1	1	yes	characteristic
397	C₂²	C₁₉×#575	1	1	yes	characteristic
398	C₂²	C₁₉×#576	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	4	4	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	2	no	—
405	C₄	C₄×#41×C₁₉	1	1	yes	characteristic
406	C₄	C₁₉×#518	1	1	yes	characteristic
407	C₄	C₁₉×#553	1	2	yes	—
408	C₂	—	4	2	no	—
409	C₂	—	8	4	no	—
410	C₂	C₁₉×#2364	1	1	yes	characteristic
411	C₂	C₁₉×#2943	1	1	yes	characteristic
412	C₂	C₁₉×#2948	1	1	yes	characteristic
413	C₂	C₁₉×#3309	1	2	yes	—
414	C₂	C₁₉×#3319	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	C₂×C₁₉×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2363	C₂	semidirect
3. C₁₉×#1936	C₂	semidirect
4. C₁₉×#1918	C₂	semidirect
5. C₁₉×#1879	C₂	semidirect
6. C₁₉×#1875	C₂	semidirect
7. C₁₉×#1762	C₂	semidirect
8. C₁₉×#1752	C₂	semidirect
9. C₁₉×#1735	C₂	semidirect
15. C₁₉×#466	C₄	semidirect
43. C₂²×C₈×C₁₉	C₂×C₄	semidirect
48. C₁₉×#121	C₂×C₄	semidirect
67. C₁₉×#107	C₂×C₄	semidirect
70. C₁₉×#102	C₂×C₄	semidirect
128. #23137	C₁₉	direct (N × H)
176. #2363	C₂×C₁₉	semidirect
177. #1936	C₂×C₁₉	semidirect
178. #1918	C₂×C₁₉	semidirect
179. #1879	C₂×C₁₉	semidirect
180. #1875	C₂×C₁₉	semidirect
181. #1762	C₂×C₁₉	semidirect
182. #1752	C₂×C₁₉	semidirect
183. #1735	C₂×C₁₉	semidirect
215. #466	C₄×C₁₉	semidirect
250. C₂²×C₈	C₂×C₄×C₁₉	semidirect
255. #121	C₂×C₄×C₁₉	semidirect
274. #107	C₂×C₄×C₁₉	semidirect
277. #102	C₂×C₄×C₁₉	semidirect
283. C₁₉	#23137	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×#466	2
C₁₉×#2363	2
C₁₉×#1936	2
C₁₉×#1918	2
C₁₉×#1879	2
C₁₉×#1875	2
C₁₉×#1762	2
C₁₉×#1752	2
C₁₉×#1735	2
#23137	19

Subgroups — C19×#23137 #18029096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23137 #18029096