Subgroups — C₁₉×#32966 #18038925

Order 4864.

1414 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#518	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#478	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2629	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1864	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1862	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1854	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1802	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1798	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1786	C₂	1	2	yes	maximal
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
12	C₁₉×#518	—	2	8	no	—
13	C₂×C₄×D₄×C₁₉	—	2	2	no	—
14	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
19	C₁₉×#478	—	2	8	no	—
20	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
21	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₁₉×#398	—	2	2	no	—
29	C₁₉×#396	—	2	2	no	—
30	C₁₉×#389	C₂²	1	2	yes	complemented
31	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#380	C₂²	1	2	yes	—
33	C₁₉×#340	C₂²	1	2	yes	complemented
34	C₁₉×#340	C₂²	1	2	yes	complemented
35	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#336	C₂²	1	1	yes	characteristic, complemented
37	C₂⁵×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	—	2	4	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	2	2	no	—
42	C₂²×D₄×C₁₉	Q₈	1	4	yes	—
43	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	—	2	2	no	—
45	C₂³×C₄×C₁₉	—	2	2	no	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
49	C₁₉×#125	—	2	4	no	—
50	C₄×D₄×C₁₉	—	2	16	no	—
51	C₄×D₄×C₁₉	—	2	4	no	—
52	C₄×D₄×C₁₉	—	2	4	no	—
53	C₄×D₄×C₁₉	—	2	4	no	—
54	C₄×D₄×C₁₉	D₄	1	8	yes	—
55	C₁₉×#117	—	2	4	no	—
56	C₁₉×#117	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
70	C₂×C₄²×C₁₉	—	2	1	no	—
71	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
73	C₁₉×#107	—	2	4	no	—
74	C₁₉×#106	—	2	4	no	—
75	C₁₉×C₄⋊C₈	—	2	4	no	—
76	C₁₉×#102	—	2	4	no	—
77	C₁₉×#102	—	2	4	no	—
78	C₁₉×#102	—	2	4	no	—
79	C₁₉×#102	—	2	4	no	—
80	C₁₉×C₂²⋊C₈	—	2	4	no	—
81	C₁₉×#95	—	2	2	no	—
82	C₁₉×#95	—	2	2	no	—
83	C₂⁴×C₁₉	—	2	4	no	—
84	C₂⁴×C₁₉	—	2	4	no	—
85	C₂⁴×C₁₉	—	2	2	no	—
86	C₂⁴×C₁₉	—	2	4	no	—
87	C₂⁴×C₁₉	—	8	2	no	—
88	C₂⁴×C₁₉	—	8	2	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	16	no	—
93	C₂×D₄×C₁₉	—	2	16	no	—
94	C₂×D₄×C₁₉	—	2	4	no	—
95	C₂×D₄×C₁₉	—	2	2	no	—
96	C₂×D₄×C₁₉	—	2	2	no	—
97	C₂×D₄×C₁₉	—	2	2	no	—
98	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
99	C₂×D₄×C₁₉	C₂×Q₈	1	4	yes	—
100	C₂×D₄×C₁₉	#41	1	4	yes	—
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	8	no	—
105	C₂²×C₄×C₁₉	—	2	8	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	2	no	—
108	C₂²×C₄×C₁₉	—	8	2	no	—
109	C₂²×C₄×C₁₉	—	8	2	no	—
110	C₂²×C₄×C₁₉	—	8	2	no	—
111	C₂²×C₄×C₁₉	—	8	2	no	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₁₉	#41	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	2	2	no	—
130	C₄⋊C₄×C₁₉	—	4	4	no	—
131	C₄⋊C₄×C₁₉	—	8	2	no	—
132	C₄⋊C₄×C₁₉	—	8	2	no	—
133	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
134	C₂²⋊C₄×C₁₉	—	2	4	no	—
135	C₂²⋊C₄×C₁₉	—	2	8	no	—
136	C₂²⋊C₄×C₁₉	—	2	4	no	—
137	C₂²⋊C₄×C₁₉	—	2	8	no	—
138	C₂²⋊C₄×C₁₉	—	8	2	no	—
139	C₄²×C₁₉	—	2	4	no	—
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	C₂×D₄	1	4	yes	—
142	#32966	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂³×C₁₉	—	2	16	no	—
144	C₂³×C₁₉	—	2	1	no	—
145	C₂³×C₁₉	—	2	4	no	—
146	C₂³×C₁₉	—	2	4	no	—
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	4	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	4	2	no	—
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	2	no	—
155	C₂³×C₁₉	—	8	8	no	—
156	C₂³×C₁₉	—	8	4	no	—
157	C₂³×C₁₉	—	8	4	no	—
158	C₂³×C₁₉	—	8	8	no	—
159	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
160	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
161	D₄×C₁₉	—	2	16	no	—
162	D₄×C₁₉	—	2	4	no	—
163	D₄×C₁₉	—	2	4	no	—
164	D₄×C₁₉	—	2	4	no	—
165	D₄×C₁₉	C₂²⋊Q₈	1	8	yes	—
166	C₂×C₄×C₁₉	—	2	1	no	—
167	C₂×C₄×C₁₉	—	2	1	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	8	8	no	—
185	C₂×C₄×C₁₉	—	8	8	no	—
186	C₂×C₄×C₁₉	#120	1	4	yes	—
187	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
188	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
191	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
192	C₈×C₁₉	—	4	2	no	—
193	C₈×C₁₉	—	4	2	no	—
194	C₂×#518	C₂×C₁₉	1	1	yes	characteristic
195	C₂×#478	C₂×C₁₉	1	2	yes	complemented
196	#2629	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#1864	C₂×C₁₉	1	2	yes	complemented
198	#1862	C₂×C₁₉	1	2	yes	complemented
199	#1854	C₂×C₁₉	1	2	yes	complemented
200	#1802	C₂×C₁₉	1	2	yes	complemented
201	#1798	C₂×C₁₉	1	1	yes	characteristic, complemented
202	#1786	C₂×C₁₉	1	2	yes	—
203	C₂²×C₁₉	—	2	4	no	—
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	2	8	no	—
206	C₂²×C₁₉	—	4	4	no	—
207	C₂²×C₁₉	—	4	4	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	4	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	—	4	4	no	—
212	C₂²×C₁₉	—	4	4	no	—
213	C₂²×C₁₉	—	4	4	no	—
214	C₂²×C₁₉	—	4	2	no	—
215	C₂²×C₁₉	—	8	16	no	—
216	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
218	C₂²×C₁₉	#525	1	1	yes	characteristic
219	C₂²×C₁₉	#576	1	2	yes	—
220	C₂²×C₁₉	#577	1	2	yes	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	—	2	4	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	4	no	—
225	C₄×C₁₉	—	8	2	no	—
226	C₄×C₁₉	—	8	2	no	—
227	C₄×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
228	C₄×C₁₉	#525	1	2	yes	—
229	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic, complemented
231	#518	—	2	8	no	—
232	C₂×C₄×D₄	—	2	2	no	—
233	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
234	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
235	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
237	C₂²×C₂²⋊C₄	—	2	2	no	—
238	#478	—	2	8	no	—
239	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
240	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
241	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
242	C₂×#102	C₂²×C₁₉	1	2	yes	—
243	C₂×#102	C₂²×C₁₉	1	2	yes	—
244	C₂×#102	C₂²×C₁₉	1	2	yes	—
245	C₂×#102	C₂²×C₁₉	1	2	yes	—
246	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
247	#398	—	2	2	no	—
248	#396	—	2	2	no	—
249	#389	C₂²×C₁₉	1	2	yes	complemented
250	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
251	#380	C₂²×C₁₉	1	2	yes	—
252	#340	C₂²×C₁₉	1	2	yes	complemented
253	#340	C₂²×C₁₉	1	2	yes	complemented
254	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
255	#336	C₂²×C₁₉	1	1	yes	characteristic, complemented
256	C₂×C₁₉	—	4	2	no	—
257	C₂×C₁₉	—	4	8	no	—
258	C₂×C₁₉	#2848	1	1	yes	characteristic
259	C₂×C₁₉	#3012	1	2	yes	—
260	C₂×C₁₉	#3081	1	2	yes	—
261	C₂×C₁₉	#3122	1	1	yes	characteristic
262	C₂×C₁₉	#3123	1	1	yes	characteristic
263	C₂⁵	—	2	1	no	—
264	C₂²×D₄	—	2	4	no	—
265	C₂²×D₄	—	2	4	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	Q₈×C₁₉	1	4	yes	—
269	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
270	C₂³×C₄	—	2	2	no	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
274	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
275	#125	—	2	4	no	—
276	C₄×D₄	—	2	16	no	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	4	no	—
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	D₄×C₁₉	1	8	yes	—
281	#117	—	2	4	no	—
282	#117	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	16	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
299	#107	—	2	4	no	—
300	#106	—	2	4	no	—
301	C₄⋊C₈	—	2	4	no	—
302	#102	—	2	4	no	—
303	#102	—	2	4	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	C₂²⋊C₈	—	2	4	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	C₁₉	#32966	1	1	yes	characteristic, direct product factor, Sylow
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	4	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	4	no	—
314	C₂⁴	—	8	2	no	—
315	C₂⁴	—	8	2	no	—
316	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	16	no	—
320	C₂×D₄	—	2	16	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
326	C₂×D₄	C₂×Q₈×C₁₉	1	4	yes	—
327	C₂×D₄	#41×C₁₉	1	4	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	8	2	no	—
336	C₂²×C₄	—	8	2	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	—	8	2	no	—
339	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
342	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
343	C₂²×C₄	#41×C₁₉	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₄⋊C₄	—	8	2	no	—
359	C₄⋊C₄	—	8	2	no	—
360	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	2	no	—
368	C₄²	C₂×D₄×C₁₉	1	4	yes	—
369	C₂³	—	2	16	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	8	8	no	—
382	C₂³	—	8	8	no	—
383	C₂³	—	8	4	no	—
384	C₂³	—	8	4	no	—
385	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
386	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
387	D₄	—	2	16	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	4	no	—
391	D₄	C₁₉×C₂²⋊Q₈	1	8	yes	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	8	8	no	—
411	C₂×C₄	—	8	8	no	—
412	C₂×C₄	C₁₉×#120	1	4	yes	—
413	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
415	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
417	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	8	16	no	—
433	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
434	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
435	C₂²	C₁₉×#525	1	1	yes	characteristic
436	C₂²	C₁₉×#576	1	2	yes	—
437	C₂²	C₁₉×#577	1	2	yes	—
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	8	2	no	—
443	C₄	—	8	2	no	—
444	C₄	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
445	C₄	C₁₉×#525	1	2	yes	—
446	C₂	—	4	2	no	—
447	C₂	—	4	8	no	—
448	C₂	C₁₉×#2848	1	1	yes	characteristic
449	C₂	C₁₉×#3012	1	2	yes	—
450	C₂	C₁₉×#3081	1	2	yes	—
451	C₂	C₁₉×#3122	1	1	yes	characteristic
452	C₂	C₁₉×#3123	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
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
2. C₂×C₁₉×#478	C₂	semidirect
3. C₁₉×#2629	C₂	semidirect
4. C₁₉×#1864	C₂	semidirect
5. C₁₉×#1862	C₂	semidirect
6. C₁₉×#1854	C₂	semidirect
7. C₁₉×#1802	C₂	semidirect
8. C₁₉×#1798	C₂	semidirect
11. C₂×C₁₉×#125	C₂²	semidirect
20. C₂×C₁₉×#107	C₂²	semidirect
21. C₂×C₁₉×#106	C₂²	semidirect
22. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
30. C₁₉×#389	C₂²	semidirect
31. C₁₉×#384	C₂²	semidirect
33. C₁₉×#340	C₂²	semidirect
34. C₁₉×#340	C₂²	semidirect
35. C₁₉×#336	C₂²	semidirect
36. C₁₉×#336	C₂²	semidirect
142. #32966	C₁₉	direct (N × H)
195. C₂×#478	C₂×C₁₉	semidirect
196. #2629	C₂×C₁₉	semidirect
197. #1864	C₂×C₁₉	semidirect
198. #1862	C₂×C₁₉	semidirect
199. #1854	C₂×C₁₉	semidirect
200. #1802	C₂×C₁₉	semidirect
201. #1798	C₂×C₁₉	semidirect
230. C₂×#125	C₂²×C₁₉	semidirect
239. C₂×#107	C₂²×C₁₉	semidirect
240. C₂×#106	C₂²×C₁₉	semidirect
241. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
249. #389	C₂²×C₁₉	semidirect
250. #384	C₂²×C₁₉	semidirect
252. #340	C₂²×C₁₉	semidirect
253. #340	C₂²×C₁₉	semidirect
254. #336	C₂²×C₁₉	semidirect
255. #336	C₂²×C₁₉	semidirect
309. C₁₉	#32966	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×#518	2
C₂×C₁₉×#478	2
C₁₉×#2629	2
C₁₉×#1864	2
C₁₉×#1862	2
C₁₉×#1854	2
C₁₉×#1802	2
C₁₉×#1798	2
C₁₉×#1786	2
#32966	19

Subgroups — C19×#32966 #18038925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32966 #18038925