Subgroups — C₁₉×#32917 #18038876

Order 4864.

1588 conjugacy classes of subgroups.

The subgroup lattice has 560 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, complemented
2	C₂×C₁₉×#463	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#447	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2620	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1879	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1877	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1802	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×D₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
18	C₁₉×#518	—	2	8	no	—
19	C₂×C₄×D₄×C₁₉	—	2	2	no	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
22	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₉	—	2	2	no	—
25	C₁₉×#463	—	2	8	no	—
26	C₁₉×#450	—	2	4	no	—
27	C₁₉×#447	—	2	4	no	—
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	complemented
29	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₂×C₁₉×#102	C₂²	1	2	yes	—
32	C₂×C₁₉×#102	C₂²	1	2	yes	complemented
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₁₉×#396	—	2	2	no	—
36	C₁₉×#394	—	2	2	no	—
37	C₁₉×#391	C₂²	1	1	yes	characteristic, complemented
38	C₁₉×#390	C₂²	1	1	yes	characteristic, complemented
39	C₁₉×#384	C₂²	1	1	yes	characteristic, complemented
40	C₁₉×#340	C₂²	1	2	yes	complemented
41	C₁₉×#340	C₂²	1	2	yes	complemented
42	C₁₉×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	4	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	D₄	1	4	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	—	2	2	no	—
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₁₉	—	2	4	no	—
57	C₂×SD₁₆×C₁₉	—	2	4	no	—
58	C₂×SD₁₆×C₁₉	—	2	4	no	—
59	C₂×D₈×C₁₉	—	2	4	no	—
60	C₂×D₈×C₁₉	—	2	4	no	—
61	C₂×D₈×C₁₉	—	2	4	no	—
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
64	C₁₉×#124	—	2	4	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₁₉×C₂²⋊Q₈	—	2	2	no	—
67	C₁₉×#121	—	2	2	no	—
68	C₁₉×#121	—	2	2	no	—
69	C₄×D₄×C₁₉	—	2	16	no	—
70	C₄×D₄×C₁₉	—	2	4	no	—
71	C₄×D₄×C₁₉	—	2	4	no	—
72	C₄×D₄×C₁₉	—	2	4	no	—
73	C₄×D₄×C₁₉	D₄	1	8	yes	complemented
74	C₁₉×#117	—	2	4	no	—
75	C₁₉×#117	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
78	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
91	C₂×C₄²×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×C₄⋊C₈	—	2	4	no	—
95	C₁₉×#103	—	2	4	no	—
96	C₁₉×#102	—	2	4	no	—
97	C₁₉×#102	—	2	4	no	—
98	C₁₉×#102	—	2	4	no	—
99	C₁₉×C₂²⋊C₈	—	2	2	no	—
100	C₁₉×C₂²⋊C₈	—	2	2	no	—
101	C₁₉×#95	—	2	2	no	—
102	C₂⁴×C₁₉	—	2	4	no	—
103	C₂⁴×C₁₉	—	2	4	no	—
104	C₂⁴×C₁₉	—	2	2	no	—
105	C₂⁴×C₁₉	—	2	4	no	—
106	C₂⁴×C₁₉	—	2	1	no	—
107	C₂⁴×C₁₉	—	8	2	no	—
108	C₂⁴×C₁₉	—	8	2	no	—
109	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	16	no	—
117	C₂×D₄×C₁₉	—	2	16	no	—
118	C₂×D₄×C₁₉	—	2	4	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	1	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	4	2	no	—
127	C₂×D₄×C₁₉	—	8	2	no	—
128	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
129	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₁₉	#41	1	4	yes	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	8	no	—
135	C₂²×C₄×C₁₉	—	2	8	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	1	no	—
139	C₂²×C₄×C₁₉	—	8	2	no	—
140	C₂²×C₄×C₁₉	—	8	2	no	—
141	C₂²×C₄×C₁₉	—	8	2	no	—
142	C₂²×C₄×C₁₉	—	8	2	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	#41	1	2	yes	—
148	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
149	SD₁₆×C₁₉	—	4	8	no	—
150	D₈×C₁₉	—	4	8	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	4	2	no	—
164	C₄⋊C₄×C₁₉	—	8	2	no	—
165	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₂²⋊C₄×C₁₉	—	2	8	no	—
168	C₂²⋊C₄×C₁₉	—	2	4	no	—
169	C₂²⋊C₄×C₁₉	—	2	8	no	—
170	C₂²⋊C₄×C₁₉	—	4	2	no	—
171	C₂²⋊C₄×C₁₉	—	4	4	no	—
172	C₂²⋊C₄×C₁₉	—	4	2	no	—
173	C₂²⋊C₄×C₁₉	—	8	2	no	—
174	C₄²×C₁₉	—	2	4	no	—
175	C₄²×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	C₂×D₄	1	4	yes	—
177	#32917	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂³×C₁₉	—	2	16	no	—
179	C₂³×C₁₉	—	2	1	no	—
180	C₂³×C₁₉	—	2	4	no	—
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	1	no	—
183	C₂³×C₁₉	—	2	4	no	—
184	C₂³×C₁₉	—	2	2	no	—
185	C₂³×C₁₉	—	2	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	1	no	—
191	C₂³×C₁₉	—	4	1	no	—
192	C₂³×C₁₉	—	4	1	no	—
193	C₂³×C₁₉	—	4	2	no	—
194	C₂³×C₁₉	—	4	2	no	—
195	C₂³×C₁₉	—	8	4	no	—
196	C₂³×C₁₉	—	8	4	no	—
197	C₂³×C₁₉	—	8	8	no	—
198	C₂³×C₁₉	—	8	8	no	—
199	C₂³×C₁₉	#121	1	2	yes	—
200	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₁₉	—	4	2	no	—
202	Q₈×C₁₉	—	4	2	no	—
203	D₄×C₁₉	—	2	16	no	—
204	D₄×C₁₉	—	2	4	no	—
205	D₄×C₁₉	—	2	4	no	—
206	D₄×C₁₉	—	2	4	no	—
207	D₄×C₁₉	—	4	2	no	—
208	D₄×C₁₉	—	4	2	no	—
209	D₄×C₁₉	—	8	4	no	—
210	D₄×C₁₉	#121	1	8	yes	—
211	C₂×C₄×C₁₉	—	2	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	4	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	4	no	—
219	C₂×C₄×C₁₉	—	2	2	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	1	no	—
224	C₂×C₄×C₁₉	—	4	1	no	—
225	C₂×C₄×C₁₉	—	4	1	no	—
226	C₂×C₄×C₁₉	—	4	1	no	—
227	C₂×C₄×C₁₉	—	4	1	no	—
228	C₂×C₄×C₁₉	—	4	2	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	8	8	no	—
231	C₂×C₄×C₁₉	—	8	8	no	—
232	C₂×C₄×C₁₉	#120	1	4	yes	—
233	C₂×C₄×C₁₉	#121	1	2	yes	—
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
237	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
238	C₈×C₁₉	—	4	2	no	—
239	C₈×C₁₉	—	4	2	no	—
240	C₂×#518	C₂×C₁₉	1	1	yes	characteristic, complemented
241	C₂×#463	C₂×C₁₉	1	2	yes	complemented
242	C₂×#450	C₂×C₁₉	1	1	yes	characteristic, complemented
243	C₂×#447	C₂×C₁₉	1	1	yes	characteristic
244	#2620	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#1879	C₂×C₁₉	1	2	yes	complemented
246	#1877	C₂×C₁₉	1	2	yes	complemented
247	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
248	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
249	#1802	C₂×C₁₉	1	2	yes	complemented
250	#1798	C₂×C₁₉	1	1	yes	characteristic, complemented
251	C₂²×C₁₉	—	2	2	no	—
252	C₂²×C₁₉	—	2	8	no	—
253	C₂²×C₁₉	—	2	2	no	—
254	C₂²×C₁₉	—	2	2	no	—
255	C₂²×C₁₉	—	4	2	no	—
256	C₂²×C₁₉	—	4	4	no	—
257	C₂²×C₁₉	—	4	4	no	—
258	C₂²×C₁₉	—	4	4	no	—
259	C₂²×C₁₉	—	4	4	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	4	4	no	—
262	C₂²×C₁₉	—	4	4	no	—
263	C₂²×C₁₉	—	8	16	no	—
264	C₂²×C₁₉	—	8	1	no	—
265	C₂²×C₁₉	—	8	2	no	—
266	C₂²×C₁₉	—	8	2	no	—
267	C₂²×C₁₉	—	8	1	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
270	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
271	C₂²×C₁₉	#525	1	1	yes	characteristic
272	C₂²×C₁₉	#576	1	2	yes	—
273	C₂²×C₁₉	#577	1	2	yes	—
274	C₄×C₁₉	—	2	2	no	—
275	C₄×C₁₉	—	2	4	no	—
276	C₄×C₁₉	—	4	2	no	—
277	C₄×C₁₉	—	4	4	no	—
278	C₄×C₁₉	—	8	1	no	—
279	C₄×C₁₉	—	8	1	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	C₂×#121	1	2	yes	—
282	C₄×C₁₉	#525	1	2	yes	—
283	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
285	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
286	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic, complemented
287	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
289	#518	—	2	8	no	—
290	C₂×C₄×D₄	—	2	2	no	—
291	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
292	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
293	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
295	C₂²×C₂²⋊C₄	—	2	2	no	—
296	#463	—	2	8	no	—
297	#450	—	2	4	no	—
298	#447	—	2	4	no	—
299	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	complemented
300	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
301	C₂×#102	C₂²×C₁₉	1	2	yes	—
302	C₂×#102	C₂²×C₁₉	1	2	yes	—
303	C₂×#102	C₂²×C₁₉	1	2	yes	complemented
304	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
305	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
306	#396	—	2	2	no	—
307	#394	—	2	2	no	—
308	#391	C₂²×C₁₉	1	1	yes	characteristic, complemented
309	#390	C₂²×C₁₉	1	1	yes	characteristic, complemented
310	#384	C₂²×C₁₉	1	1	yes	characteristic, complemented
311	#340	C₂²×C₁₉	1	2	yes	complemented
312	#340	C₂²×C₁₉	1	2	yes	complemented
313	#336	C₂²×C₁₉	1	2	yes	complemented
314	C₂×C₁₉	—	4	2	no	—
315	C₂×C₁₉	—	4	8	no	—
316	C₂×C₁₉	—	16	1	no	—
317	C₂×C₁₉	#2847	1	1	yes	characteristic
318	C₂×C₁₉	#3012	1	2	yes	—
319	C₂×C₁₉	#3041	1	1	yes	characteristic
320	C₂×C₁₉	#3042	1	1	yes	characteristic
321	C₂×C₁₉	#3118	1	2	yes	—
322	C₂⁵	—	2	1	no	—
323	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
324	C₂²×D₄	—	2	4	no	—
325	C₂²×D₄	—	2	4	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	D₄×C₁₉	1	4	yes	—
330	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
332	C₂³×C₄	—	2	2	no	—
333	C₂³×C₄	—	2	2	no	—
334	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
335	C₂×SD₁₆	—	2	4	no	—
336	C₂×SD₁₆	—	2	4	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×D₈	—	2	4	no	—
339	C₂×D₈	—	2	4	no	—
340	C₂×D₈	—	2	4	no	—
341	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
342	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
343	#124	—	2	4	no	—
344	C₂²⋊Q₈	—	2	2	no	—
345	C₂²⋊Q₈	—	2	2	no	—
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	C₄×D₄	—	2	16	no	—
349	C₄×D₄	—	2	4	no	—
350	C₄×D₄	—	2	4	no	—
351	C₄×D₄	—	2	4	no	—
352	C₄×D₄	D₄×C₁₉	1	8	yes	complemented
353	#117	—	2	4	no	—
354	#117	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
361	C₂×C₂²⋊C₄	—	2	16	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
373	C₄⋊C₈	—	2	4	no	—
374	#103	—	2	4	no	—
375	#102	—	2	4	no	—
376	#102	—	2	4	no	—
377	#102	—	2	4	no	—
378	C₂²⋊C₈	—	2	2	no	—
379	C₂²⋊C₈	—	2	2	no	—
380	#95	—	2	2	no	—
381	C₁₉	#32917	1	1	yes	characteristic, direct product factor, Sylow
382	C₂⁴	—	2	4	no	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	2	no	—
385	C₂⁴	—	2	4	no	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	—	8	2	no	—
388	C₂⁴	—	8	2	no	—
389	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	16	no	—
397	C₂×D₄	—	2	16	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	8	2	no	—
408	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
409	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
410	C₂×D₄	#41×C₁₉	1	4	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	8	2	no	—
420	C₂²×C₄	—	8	2	no	—
421	C₂²×C₄	—	8	2	no	—
422	C₂²×C₄	—	8	2	no	—
423	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
427	C₂²×C₄	#41×C₁₉	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
429	SD₁₆	—	4	8	no	—
430	D₈	—	4	8	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	—	8	2	no	—
445	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₂²⋊C₄	—	4	4	no	—
452	C₂²⋊C₄	—	4	2	no	—
453	C₂²⋊C₄	—	8	2	no	—
454	C₄²	—	2	4	no	—
455	C₄²	—	2	2	no	—
456	C₄²	C₂×D₄×C₁₉	1	4	yes	—
457	C₂³	—	2	16	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	8	4	no	—
475	C₂³	—	8	4	no	—
476	C₂³	—	8	8	no	—
477	C₂³	—	8	8	no	—
478	C₂³	C₁₉×#121	1	2	yes	—
479	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	D₄	—	2	16	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	4	no	—
485	D₄	—	2	4	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	2	no	—
488	D₄	—	8	4	no	—
489	D₄	C₁₉×#121	1	8	yes	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	8	8	no	—
510	C₂×C₄	—	8	8	no	—
511	C₂×C₄	C₁₉×#120	1	4	yes	—
512	C₂×C₄	C₁₉×#121	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
515	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
516	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
517	C₈	—	4	2	no	—
518	C₈	—	4	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	8	16	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	2	no	—
537	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
538	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
539	C₂²	C₁₉×#525	1	1	yes	characteristic
540	C₂²	C₁₉×#576	1	2	yes	—
541	C₂²	C₁₉×#577	1	2	yes	—
542	C₄	—	2	4	no	—
543	C₄	—	2	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	4	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	C₂×C₁₉×#121	1	2	yes	—
550	C₄	C₁₉×#525	1	2	yes	—
551	C₂	—	4	2	no	—
552	C₂	—	4	8	no	—
553	C₂	—	16	1	no	—
554	C₂	C₁₉×#2847	1	1	yes	characteristic
555	C₂	C₁₉×#3012	1	2	yes	—
556	C₂	C₁₉×#3041	1	1	yes	characteristic
557	C₂	C₁₉×#3042	1	1	yes	characteristic
558	C₂	C₁₉×#3118	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#447	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. C₂×C₁₉×#518	C₂	semidirect
2. C₂×C₁₉×#463	C₂	semidirect
3. C₂×C₁₉×#450	C₂	semidirect
5. C₁₉×#2620	C₂	semidirect
6. C₁₉×#1879	C₂	semidirect
7. C₁₉×#1877	C₂	semidirect
8. C₁₉×#1875	C₂	semidirect
9. C₁₉×#1873	C₂	semidirect
10. C₁₉×#1802	C₂	semidirect
11. C₁₉×#1798	C₂	semidirect
15. C₂×C₁₉×#124	C₂²	semidirect
28. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
29. C₂×C₁₉×#103	C₂²	semidirect
32. C₂×C₁₉×#102	C₂²	semidirect
37. C₁₉×#391	C₂²	semidirect
38. C₁₉×#390	C₂²	semidirect
39. C₁₉×#384	C₂²	semidirect
40. C₁₉×#340	C₂²	semidirect
41. C₁₉×#340	C₂²	semidirect
42. C₁₉×#336	C₂²	semidirect
73. C₄×D₄×C₁₉	D₄	semidirect
177. #32917	C₁₉	direct (N × H)
240. C₂×#518	C₂×C₁₉	semidirect
241. C₂×#463	C₂×C₁₉	semidirect
242. C₂×#450	C₂×C₁₉	semidirect
244. #2620	C₂×C₁₉	semidirect
245. #1879	C₂×C₁₉	semidirect
246. #1877	C₂×C₁₉	semidirect
247. #1875	C₂×C₁₉	semidirect
248. #1873	C₂×C₁₉	semidirect
249. #1802	C₂×C₁₉	semidirect
250. #1798	C₂×C₁₉	semidirect
286. C₂×#124	C₂²×C₁₉	semidirect
299. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
300. C₂×#103	C₂²×C₁₉	semidirect
303. C₂×#102	C₂²×C₁₉	semidirect
308. #391	C₂²×C₁₉	semidirect
309. #390	C₂²×C₁₉	semidirect
310. #384	C₂²×C₁₉	semidirect
311. #340	C₂²×C₁₉	semidirect
312. #340	C₂²×C₁₉	semidirect
313. #336	C₂²×C₁₉	semidirect
352. C₄×D₄	D₄×C₁₉	semidirect
381. C₁₉	#32917	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×#463	2
C₂×C₁₉×#450	2
C₂×C₁₉×#447	2
C₁₉×#2620	2
C₁₉×#1879	2
C₁₉×#1877	2
C₁₉×#1875	2
C₁₉×#1873	2
C₁₉×#1802	2
C₁₉×#1798	2
#32917	19

Subgroups — C19×#32917 #18038876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32917 #18038876