Subgroups — C₁₉×#60425 #18066384

Order 4864.

2750 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#575	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3046	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3045	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3037	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3036	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#417	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₁₉	C₂²	1	2	yes	—
11	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#575	—	2	16	no	—
13	C₂×C₁₉×#137	C₂²	1	4	yes	complemented
14	C₂×C₁₉×#137	C₂²	1	4	yes	complemented
15	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
16	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
17	C₂×C₁₉×#135	C₂²	1	8	yes	—
18	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
19	C₁₉×#537	—	2	1	no	—
20	C₁₉×#537	—	2	1	no	—
21	C₁₉×#536	C₂²	1	4	yes	complemented
22	C₁₉×#535	C₂²	1	4	yes	complemented
23	C₁₉×#534	—	2	2	no	—
24	C₁₉×#532	C₂²	1	4	yes	—
25	C₁₉×#525	—	2	4	no	—
26	C₁₉×#520	—	2	4	no	—
27	C₁₉×#520	C₂²	1	8	yes	complemented
28	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₁₉	—	2	2	no	—
30	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
31	C₂×C₁₉×#117	—	2	1	no	—
32	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₁₉×#464	C₂²	1	16	yes	complemented
36	C₁₉×#463	C₂²	1	16	yes	complemented
37	C₁₉×#462	C₂²	1	8	yes	complemented
38	C₁₉×#461	C₂²	1	8	yes	complemented
39	C₁₉×#460	C₂²	1	8	yes	complemented
40	C₁₉×#459	C₂²	1	8	yes	complemented
41	C₁₉×#424	C₂²	1	8	yes	complemented
42	C₁₉×#423	C₂²	1	4	yes	complemented
43	C₁₉×#417	C₂²	1	8	yes	complemented
44	C₁₉×#417	C₂²	1	8	yes	complemented
45	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
46	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	—	2	4	no	—
51	C₂×#41×C₁₉	—	2	8	no	—
52	C₂×#41×C₁₉	—	2	8	no	—
53	C₂×#41×C₁₉	D₄	1	8	yes	complemented
54	C₂×#41×C₁₉	C₂³	1	4	yes	—
55	C₂×#41×C₁₉	C₂³	1	4	yes	—
56	C₂×#41×C₁₉	C₂³	1	4	yes	—
57	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
58	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₉	—	2	1	no	—
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	—	2	2	no	—
66	C₂³×C₄×C₁₉	—	2	2	no	—
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₁₉×#137	—	2	16	no	—
69	C₁₉×#137	—	2	16	no	—
70	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
71	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
72	C₁₉×#135	—	2	32	no	—
73	C₂×Q₁₆×C₁₉	C₂³	1	8	yes	—
74	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
75	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
76	C₂×D₈×C₁₉	C₂³	1	8	yes	—
77	C₂×M₁₆×C₁₉	—	2	8	no	—
78	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
79	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
80	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
81	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₁₉×#127	C₂³	1	4	yes	—
83	C₁₉×#124	C₂³	1	8	yes	—
84	C₁₉×#123	—	2	8	no	—
85	C₁₉×C₂²⋊Q₈	—	2	4	no	—
86	C₁₉×C₂²⋊Q₈	—	2	4	no	—
87	C₁₉×#121	—	2	4	no	—
88	C₁₉×#121	—	2	4	no	—
89	C₁₉×#121	—	2	4	no	—
90	C₁₉×#121	—	2	4	no	—
91	C₁₉×#120	—	2	8	no	—
92	C₄×Q₈×C₁₉	—	2	4	no	—
93	C₄×Q₈×C₁₉	C₂³	1	8	yes	—
94	C₄×D₄×C₁₉	—	2	16	no	—
95	C₄×D₄×C₁₉	—	2	4	no	—
96	C₄×D₄×C₁₉	—	2	4	no	—
97	C₄×D₄×C₁₉	—	2	4	no	—
98	C₄×D₄×C₁₉	C₂³	1	8	yes	—
99	C₁₉×#117	—	2	8	no	—
100	C₁₉×#117	D₄	1	4	yes	—
101	C₁₉×#117	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
106	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
112	C₂×C₄²×C₁₉	—	2	2	no	—
113	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
114	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
115	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
116	C₁₉×#103	C₂³	1	16	yes	—
117	C₁₉×#102	C₂³	1	16	yes	—
118	C₂⁴×C₁₉	—	2	1	no	—
119	C₂⁴×C₁₉	—	2	2	no	—
120	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
121	#41×C₁₉	—	2	16	no	—
122	#41×C₁₉	—	2	8	no	—
123	#41×C₁₉	—	2	8	no	—
124	#41×C₁₉	—	2	8	no	—
125	#41×C₁₉	—	2	8	no	—
126	#41×C₁₉	—	2	8	no	—
127	#41×C₁₉	—	4	8	no	—
128	#41×C₁₉	—	4	8	no	—
129	#41×C₁₉	C₂×D₄	1	16	yes	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	2	2	no	—
132	C₂×Q₈×C₁₉	—	2	2	no	—
133	C₂×Q₈×C₁₉	—	2	4	no	—
134	C₂×Q₈×C₁₉	—	2	4	no	—
135	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
136	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
137	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
138	C₂×D₄×C₁₉	—	2	8	no	—
139	C₂×D₄×C₁₉	—	2	4	no	—
140	C₂×D₄×C₁₉	—	2	4	no	—
141	C₂×D₄×C₁₉	—	2	4	no	—
142	C₂×D₄×C₁₉	—	2	1	no	—
143	C₂×D₄×C₁₉	—	2	4	no	—
144	C₂×D₄×C₁₉	—	2	2	no	—
145	C₂×D₄×C₁₉	—	2	4	no	—
146	C₂×D₄×C₁₉	—	2	4	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	4	no	—
149	C₂×D₄×C₁₉	—	4	8	no	—
150	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
151	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
152	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	8	no	—
155	C₂²×C₄×C₁₉	—	2	4	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	4	no	—
159	C₂²×C₄×C₁₉	—	2	4	no	—
160	C₂²×C₄×C₁₉	—	2	4	no	—
161	C₂²×C₄×C₁₉	—	2	8	no	—
162	C₂²×C₄×C₁₉	—	4	8	no	—
163	C₂²×C₄×C₁₉	—	8	4	no	—
164	C₂²×C₄×C₁₉	—	8	2	no	—
165	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₉	#41	1	4	yes	—
171	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
173	Q₁₆×C₁₉	—	2	16	no	—
174	SD₁₆×C₁₉	—	2	16	no	—
175	SD₁₆×C₁₉	—	2	16	no	—
176	D₈×C₁₉	—	2	16	no	—
177	M₁₆×C₁₉	—	2	8	no	—
178	M₁₆×C₁₉	—	2	8	no	—
179	C₂×C₈×C₁₉	—	2	8	no	—
180	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
181	C₄⋊C₄×C₁₉	—	2	4	no	—
182	C₄⋊C₄×C₁₉	—	2	8	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	4	no	—
185	C₄⋊C₄×C₁₉	—	2	4	no	—
186	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
187	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
188	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
189	C₂²⋊C₄×C₁₉	—	2	8	no	—
190	C₂²⋊C₄×C₁₉	—	2	8	no	—
191	C₂²⋊C₄×C₁₉	—	2	8	no	—
192	C₂²⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
193	C₄²×C₁₉	—	2	8	no	—
194	C₄²×C₁₉	C₂×D₄	1	4	yes	—
195	C₄²×C₁₉	C₂⁴	1	4	yes	—
196	#60425	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂³×C₁₉	—	2	4	no	—
198	C₂³×C₁₉	—	2	2	no	—
199	C₂³×C₁₉	—	2	4	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	4	no	—
205	C₂³×C₁₉	—	8	2	no	—
206	C₂³×C₁₉	—	8	2	no	—
207	C₂³×C₁₉	#121	1	4	yes	—
208	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
209	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
210	Q₈×C₁₉	—	2	4	no	—
211	Q₈×C₁₉	—	2	2	no	—
212	Q₈×C₁₉	—	2	4	no	—
213	Q₈×C₁₉	—	2	4	no	—
214	Q₈×C₁₉	—	4	4	no	—
215	Q₈×C₁₉	C₂²×D₄	1	4	yes	—
216	D₄×C₁₉	—	2	16	no	—
217	D₄×C₁₉	—	2	4	no	—
218	D₄×C₁₉	—	2	4	no	—
219	D₄×C₁₉	—	2	2	no	—
220	D₄×C₁₉	—	2	4	no	—
221	D₄×C₁₉	—	4	8	no	—
222	D₄×C₁₉	—	4	8	no	—
223	D₄×C₁₉	—	4	4	no	—
224	D₄×C₁₉	—	8	4	no	—
225	D₄×C₁₉	—	8	4	no	—
226	D₄×C₁₉	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	16	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	4	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	4	no	—
235	C₂×C₄×C₁₉	—	4	4	no	—
236	C₂×C₄×C₁₉	—	4	8	no	—
237	C₂×C₄×C₁₉	—	4	8	no	—
238	C₂×C₄×C₁₉	—	8	8	no	—
239	C₂×C₄×C₁₉	—	8	4	no	—
240	C₂×C₄×C₁₉	#121	1	4	yes	—
241	C₂×C₄×C₁₉	#121	1	8	yes	—
242	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
243	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
249	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
250	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
251	C₈×C₁₉	—	2	8	no	—
252	C₂×#575	C₂×C₁₉	1	2	yes	complemented
253	#3449	C₂×C₁₉	1	1	yes	characteristic, complemented
254	C₂×#520	C₂×C₁₉	1	1	yes	characteristic, complemented
255	#3046	C₂×C₁₉	1	8	yes	complemented
256	#3045	C₂×C₁₉	1	8	yes	complemented
257	#3037	C₂×C₁₉	1	4	yes	complemented
258	#3036	C₂×C₁₉	1	4	yes	complemented
259	#2905	C₂×C₁₉	1	1	yes	characteristic, complemented
260	C₂×#417	C₂×C₁₉	1	2	yes	complemented
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	2	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	2	no	—
265	C₂²×C₁₉	—	2	4	no	—
266	C₂²×C₁₉	—	4	4	no	—
267	C₂²×C₁₉	—	4	8	no	—
268	C₂²×C₁₉	—	4	2	no	—
269	C₂²×C₁₉	—	4	2	no	—
270	C₂²×C₁₉	—	4	4	no	—
271	C₂²×C₁₉	—	4	4	no	—
272	C₂²×C₁₉	—	4	4	no	—
273	C₂²×C₁₉	—	8	8	no	—
274	C₂²×C₁₉	C₂×#121	1	2	yes	—
275	C₂²×C₁₉	C₂×#121	1	4	yes	—
276	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
277	C₄×C₁₉	—	2	4	no	—
278	C₄×C₁₉	—	2	4	no	—
279	C₄×C₁₉	—	2	4	no	—
280	C₄×C₁₉	—	4	4	no	—
281	C₄×C₁₉	—	4	4	no	—
282	C₄×C₁₉	C₂×#121	1	4	yes	—
283	C₄×C₁₉	C₂×#121	1	2	yes	—
284	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
285	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
286	C₂²×#41	C₂²×C₁₉	1	2	yes	—
287	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
288	#575	—	2	16	no	—
289	C₂×#137	C₂²×C₁₉	1	4	yes	complemented
290	C₂×#137	C₂²×C₁₉	1	4	yes	complemented
291	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
292	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
293	C₂×#135	C₂²×C₁₉	1	8	yes	—
294	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
295	#537	—	2	1	no	—
296	#537	—	2	1	no	—
297	#536	C₂²×C₁₉	1	4	yes	complemented
298	#535	C₂²×C₁₉	1	4	yes	complemented
299	#534	—	2	2	no	—
300	#532	C₂²×C₁₉	1	4	yes	—
301	#525	—	2	4	no	—
302	#520	—	2	4	no	—
303	#520	C₂²×C₁₉	1	8	yes	complemented
304	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
305	C₂×C₄×D₄	—	2	2	no	—
306	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	complemented
307	C₂×#117	—	2	1	no	—
308	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	—	2	1	no	—
310	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
311	#464	C₂²×C₁₉	1	16	yes	complemented
312	#463	C₂²×C₁₉	1	16	yes	complemented
313	#462	C₂²×C₁₉	1	8	yes	complemented
314	#461	C₂²×C₁₉	1	8	yes	complemented
315	#460	C₂²×C₁₉	1	8	yes	complemented
316	#459	C₂²×C₁₉	1	8	yes	complemented
317	#424	C₂²×C₁₉	1	8	yes	complemented
318	#423	C₂²×C₁₉	1	4	yes	complemented
319	#417	C₂²×C₁₉	1	8	yes	complemented
320	#417	C₂²×C₁₉	1	8	yes	complemented
321	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
322	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
323	C₂×C₁₉	—	2	2	no	—
324	C₂×C₁₉	—	2	4	no	—
325	C₂×C₁₉	—	4	4	no	—
326	C₂×C₁₉	—	8	4	no	—
327	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
328	C₂×C₁₉	#3585	1	1	yes	characteristic
329	C₂×C₁₉	#3586	1	1	yes	characteristic
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	4	no	—
334	C₂×#41	—	2	8	no	—
335	C₂×#41	—	2	8	no	—
336	C₂×#41	D₄×C₁₉	1	8	yes	complemented
337	C₂×#41	C₂³×C₁₉	1	4	yes	—
338	C₂×#41	C₂³×C₁₉	1	4	yes	—
339	C₂×#41	C₂³×C₁₉	1	4	yes	—
340	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
341	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
345	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	—	2	2	no	—
349	C₂³×C₄	—	2	2	no	—
350	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
351	#137	—	2	16	no	—
352	#137	—	2	16	no	—
353	AGL(1,ℤ/8)	—	2	16	no	—
354	AGL(1,ℤ/8)	—	2	16	no	—
355	#135	—	2	32	no	—
356	C₂×Q₁₆	C₂³×C₁₉	1	8	yes	—
357	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
358	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
359	C₂×D₈	C₂³×C₁₉	1	8	yes	—
360	C₂×M₁₆	—	2	8	no	—
361	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
362	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
363	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
364	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
365	#127	C₂³×C₁₉	1	4	yes	—
366	#124	C₂³×C₁₉	1	8	yes	—
367	#123	—	2	8	no	—
368	C₂²⋊Q₈	—	2	4	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	#121	—	2	4	no	—
371	#121	—	2	4	no	—
372	#121	—	2	4	no	—
373	#121	—	2	4	no	—
374	#120	—	2	8	no	—
375	C₄×Q₈	—	2	4	no	—
376	C₄×Q₈	C₂³×C₁₉	1	8	yes	—
377	C₄×D₄	—	2	16	no	—
378	C₄×D₄	—	2	4	no	—
379	C₄×D₄	—	2	4	no	—
380	C₄×D₄	—	2	4	no	—
381	C₄×D₄	C₂³×C₁₉	1	8	yes	—
382	#117	—	2	8	no	—
383	#117	D₄×C₁₉	1	4	yes	—
384	#117	C₂³×C₁₉	1	4	yes	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	8	no	—
389	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
390	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
395	C₂×C₄²	—	2	2	no	—
396	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
397	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
398	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
399	#103	C₂³×C₁₉	1	16	yes	—
400	#102	C₂³×C₁₉	1	16	yes	—
401	C₁₉	#60425	1	1	yes	characteristic, direct product factor, Sylow
402	C₂⁴	—	2	1	no	—
403	C₂⁴	—	2	2	no	—
404	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
405	#41	—	2	16	no	—
406	#41	—	2	8	no	—
407	#41	—	2	8	no	—
408	#41	—	2	8	no	—
409	#41	—	2	8	no	—
410	#41	—	2	8	no	—
411	#41	—	4	8	no	—
412	#41	—	4	8	no	—
413	#41	C₂×D₄×C₁₉	1	16	yes	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
420	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
421	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	4	8	no	—
434	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
435	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
436	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	4	8	no	—
447	C₂²×C₄	—	8	4	no	—
448	C₂²×C₄	—	8	2	no	—
449	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
450	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
451	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
454	C₂²×C₄	#41×C₁₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
457	Q₁₆	—	2	16	no	—
458	SD₁₆	—	2	16	no	—
459	SD₁₆	—	2	16	no	—
460	D₈	—	2	16	no	—
461	M₁₆	—	2	8	no	—
462	M₁₆	—	2	8	no	—
463	C₂×C₈	—	2	8	no	—
464	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
471	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
472	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
477	C₄²	—	2	8	no	—
478	C₄²	C₂×D₄×C₁₉	1	4	yes	—
479	C₄²	C₂⁴×C₁₉	1	4	yes	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	8	2	no	—
489	C₂³	—	8	2	no	—
490	C₂³	C₁₉×#121	1	4	yes	—
491	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
492	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
493	Q₈	—	2	4	no	—
494	Q₈	—	2	2	no	—
495	Q₈	—	2	4	no	—
496	Q₈	—	2	4	no	—
497	Q₈	—	4	4	no	—
498	Q₈	C₂²×D₄×C₁₉	1	4	yes	—
499	D₄	—	2	16	no	—
500	D₄	—	2	4	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	2	no	—
503	D₄	—	2	4	no	—
504	D₄	—	4	8	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	4	no	—
507	D₄	—	8	4	no	—
508	D₄	—	8	4	no	—
509	D₄	C₂²×D₄×C₁₉	1	4	yes	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	16	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	—	8	8	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	C₁₉×#121	1	4	yes	—
524	C₂×C₄	C₁₉×#121	1	8	yes	—
525	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
527	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
530	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
531	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
532	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
533	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
534	C₈	—	2	8	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	8	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	8	8	no	—
548	C₂²	C₂×C₁₉×#121	1	2	yes	—
549	C₂²	C₂×C₁₉×#121	1	4	yes	—
550	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
551	C₄	—	2	4	no	—
552	C₄	—	2	4	no	—
553	C₄	—	2	4	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	4	no	—
556	C₄	C₂×C₁₉×#121	1	4	yes	—
557	C₄	C₂×C₁₉×#121	1	2	yes	—
558	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
559	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
560	C₂	—	2	2	no	—
561	C₂	—	2	4	no	—
562	C₂	—	4	4	no	—
563	C₂	—	8	4	no	—
564	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
565	C₂	C₁₉×#3585	1	1	yes	characteristic
566	C₂	C₁₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#575	C₂	semidirect
2. C₁₉×#3449	C₂	semidirect
3. C₂×C₁₉×#520	C₂	semidirect
4. C₁₉×#3046	C₂	semidirect
5. C₁₉×#3045	C₂	semidirect
6. C₁₉×#3037	C₂	semidirect
7. C₁₉×#3036	C₂	semidirect
8. C₁₉×#2905	C₂	semidirect
9. C₂×C₁₉×#417	C₂	semidirect
13. C₂×C₁₉×#137	C₂²	semidirect
14. C₂×C₁₉×#137	C₂²	semidirect
15. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
16. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
21. C₁₉×#536	C₂²	semidirect
22. C₁₉×#535	C₂²	semidirect
27. C₁₉×#520	C₂²	semidirect
28. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
30. C₂×C₄×D₄×C₁₉	C₂²	semidirect
35. C₁₉×#464	C₂²	semidirect
36. C₁₉×#463	C₂²	semidirect
37. C₁₉×#462	C₂²	semidirect
38. C₁₉×#461	C₂²	semidirect
39. C₁₉×#460	C₂²	semidirect
40. C₁₉×#459	C₂²	semidirect
41. C₁₉×#424	C₂²	semidirect
42. C₁₉×#423	C₂²	semidirect
43. C₁₉×#417	C₂²	semidirect
44. C₁₉×#417	C₂²	semidirect
45. C₂×C₁₉×#103	C₂²	semidirect
46. C₂×C₁₉×#102	C₂²	semidirect
53. C₂×#41×C₁₉	D₄	semidirect
196. #60425	C₁₉	direct (N × H)
252. C₂×#575	C₂×C₁₉	semidirect
253. #3449	C₂×C₁₉	semidirect
254. C₂×#520	C₂×C₁₉	semidirect
255. #3046	C₂×C₁₉	semidirect
256. #3045	C₂×C₁₉	semidirect
257. #3037	C₂×C₁₉	semidirect
258. #3036	C₂×C₁₉	semidirect
259. #2905	C₂×C₁₉	semidirect
260. C₂×#417	C₂×C₁₉	semidirect
289. C₂×#137	C₂²×C₁₉	semidirect
290. C₂×#137	C₂²×C₁₉	semidirect
291. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
292. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
297. #536	C₂²×C₁₉	semidirect
298. #535	C₂²×C₁₉	semidirect
303. #520	C₂²×C₁₉	semidirect
304. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
306. C₂×C₄×D₄	C₂²×C₁₉	semidirect
311. #464	C₂²×C₁₉	semidirect
312. #463	C₂²×C₁₉	semidirect
313. #462	C₂²×C₁₉	semidirect
314. #461	C₂²×C₁₉	semidirect
315. #460	C₂²×C₁₉	semidirect
316. #459	C₂²×C₁₉	semidirect
317. #424	C₂²×C₁₉	semidirect
318. #423	C₂²×C₁₉	semidirect
319. #417	C₂²×C₁₉	semidirect
320. #417	C₂²×C₁₉	semidirect
321. C₂×#103	C₂²×C₁₉	semidirect
322. C₂×#102	C₂²×C₁₉	semidirect
336. C₂×#41	D₄×C₁₉	semidirect
401. C₁₉	#60425	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×#575	2
C₁₉×#3449	2
C₂×C₁₉×#520	2
C₁₉×#3046	2
C₁₉×#3045	2
C₁₉×#3037	2
C₁₉×#3036	2
C₁₉×#2905	2
C₂×C₁₉×#417	2
#60425	19

Subgroups — C19×#60425 #18066384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60425 #18066384