Subgroups — C₁₉×#22454 #18028413

Order 4864.

1380 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#443	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2880	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1974	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1876	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1810	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1789	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	2	yes	—
10	C₂×C₁₉×#135	—	2	8	no	—
11	C₂×C₁₉×#135	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₉×#135	C₄	1	2	yes	complemented
13	C₂×C₁₉×#135	C₄	1	1	yes	characteristic, complemented
14	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#135	C₂²	1	2	yes	—
16	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₉	C₄	1	1	yes	characteristic, complemented
18	C₂²×SD₁₆×C₁₉	C₄	1	2	yes	complemented
19	C₂²×D₈×C₁₉	C₄	1	1	yes	characteristic, complemented
20	C₂×C₁₉×#131	C₂²	1	4	yes	complemented
21	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#443	—	2	8	no	—
23	C₂×C₁₉×#108	C₂²	1	2	yes	complemented
24	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
25	C₂×C₁₉×#104	C₂²	1	4	yes	complemented
26	C₁₉×#408	—	2	4	no	—
27	C₁₉×#408	C₂²	1	4	yes	complemented
28	C₁₉×#407	—	2	2	no	—
29	C₁₉×#407	C₂²	1	2	yes	—
30	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₉	C₂²	1	2	yes	complemented
33	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₁₉×#341	C₂²	1	2	yes	complemented
35	C₁₉×#336	C₂²	1	2	yes	complemented
36	C₂×#41×C₁₉	—	2	2	no	—
37	C₂×#41×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	8	no	—
39	C₂×#41×C₁₉	—	4	4	no	—
40	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×#41×C₁₉	C₂³	1	2	yes	—
43	C₂×#41×C₁₉	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₉	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₁₉×#135	—	2	8	no	—
50	C₁₉×#135	—	2	4	no	—
51	C₁₉×#135	—	2	8	no	—
52	C₁₉×#135	—	2	4	no	—
53	C₁₉×#135	—	2	4	no	—
54	C₁₉×#135	D₄	1	8	yes	—
55	C₂×Q₁₆×C₁₉	—	2	4	no	—
56	C₂×Q₁₆×C₁₉	C₂×C₄	1	2	yes	—
57	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
58	C₂×Q₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
59	C₂×SD₁₆×C₁₉	—	2	8	no	—
60	C₂×SD₁₆×C₁₉	C₂×C₄	1	2	yes	—
61	C₂×SD₁₆×C₁₉	C₂×C₄	1	2	yes	—
62	C₂×SD₁₆×C₁₉	C₂×C₄	1	2	yes	—
63	C₂×SD₁₆×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×D₈×C₁₉	—	2	4	no	—
65	C₂×D₈×C₁₉	C₂×C₄	1	2	yes	—
66	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×D₈×C₁₉	C₂×C₄	1	1	yes	characteristic
68	C₁₉×#131	—	2	8	no	—
69	C₁₉×#131	—	4	4	no	—
70	C₂×M₁₆×C₁₉	—	2	4	no	—
71	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₉	—	2	4	no	—
73	C₂²×C₈×C₁₉	—	2	4	no	—
74	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
83	C₁₉×#108	—	2	4	no	—
84	C₁₉×#104	—	2	8	no	—
85	C₁₉×#104	—	4	4	no	—
86	C₁₉×C₂²⋊C₈	—	2	2	no	—
87	C₁₉×C₂²⋊C₈	—	2	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	4	no	—
89	C₁₉×C₂²⋊C₈	—	2	4	no	—
90	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
91	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
92	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
93	C₄×C₈×C₁₉	—	2	4	no	—
94	C₁₉×#95	—	2	1	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	#41	1	1	yes	characteristic
97	#41×C₁₉	—	2	4	no	—
98	#41×C₁₉	—	2	4	no	—
99	#41×C₁₉	—	2	4	no	—
100	#41×C₁₉	—	2	4	no	—
101	#41×C₁₉	—	2	4	no	—
102	#41×C₁₉	—	4	8	no	—
103	#41×C₁₉	—	4	2	no	—
104	#41×C₁₉	—	4	2	no	—
105	#41×C₁₉	—	4	8	no	—
106	#41×C₁₉	C₂×D₄	1	8	yes	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	—	2	4	no	—
109	C₂×Q₈×C₁₉	—	4	2	no	—
110	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
111	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	2	2	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	2	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	4	2	no	—
119	C₂×D₄×C₁₉	—	4	8	no	—
120	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	2	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	4	8	no	—
131	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₁₉	—	2	4	no	—
138	Q₁₆×C₁₉	—	2	2	no	—
139	Q₁₆×C₁₉	C₂²⋊C₄	1	4	yes	complemented
140	SD₁₆×C₁₉	—	2	4	no	—
141	SD₁₆×C₁₉	—	2	4	no	—
142	SD₁₆×C₁₉	—	2	4	no	—
143	SD₁₆×C₁₉	C₂²⋊C₄	1	8	yes	complemented
144	D₈×C₁₉	—	2	4	no	—
145	D₈×C₁₉	—	2	2	no	—
146	D₈×C₁₉	C₂²⋊C₄	1	4	yes	complemented
147	M₁₆×C₁₉	—	2	4	no	—
148	M₁₆×C₁₉	—	2	4	no	—
149	M₁₆×C₁₉	—	4	8	no	—
150	C₂×C₈×C₁₉	—	2	2	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	C₂×C₈×C₁₉	—	2	4	no	—
158	C₂×C₈×C₁₉	—	4	8	no	—
159	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
166	C₂²⋊C₄×C₁₉	—	2	4	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	#22454	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	4	no	—
176	C₂³×C₁₉	—	4	4	no	—
177	C₂³×C₁₉	—	8	2	no	—
178	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
179	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
180	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
181	Q₈×C₁₉	—	2	2	no	—
182	Q₈×C₁₉	—	2	2	no	—
183	Q₈×C₁₉	—	2	2	no	—
184	Q₈×C₁₉	—	4	4	no	—
185	Q₈×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
186	D₄×C₁₉	—	2	8	no	—
187	D₄×C₁₉	—	2	2	no	—
188	D₄×C₁₉	—	2	2	no	—
189	D₄×C₁₉	—	2	2	no	—
190	D₄×C₁₉	—	4	4	no	—
191	D₄×C₁₉	—	4	4	no	—
192	D₄×C₁₉	—	4	4	no	—
193	D₄×C₁₉	—	4	4	no	—
194	D₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	2	8	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	4	no	—
208	C₂×C₄×C₁₉	—	4	4	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	4	no	—
212	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
218	C₈×C₁₉	—	2	1	no	—
219	C₈×C₁₉	—	2	1	no	—
220	C₈×C₁₉	—	2	2	no	—
221	C₈×C₁₉	—	2	2	no	—
222	C₈×C₁₉	—	4	4	no	—
223	C₈×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
224	C₈×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
225	C₂²×#135	C₂×C₁₉	1	1	yes	characteristic
226	C₂×#443	C₂×C₁₉	1	2	yes	complemented
227	#2880	C₂×C₁₉	1	2	yes	complemented
228	#1974	C₂×C₁₉	1	2	yes	complemented
229	#1876	C₂×C₁₉	1	4	yes	complemented
230	#1810	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1789	C₂×C₁₉	1	2	yes	complemented
232	C₈×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	4	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	1	no	—
241	C₂²×C₁₉	—	4	4	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	4	2	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	8	8	no	—
248	C₂²×C₁₉	#443	1	2	yes	complemented
249	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂²×C₁₉	#546	1	2	yes	—
251	C₄×C₁₉	—	2	1	no	—
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	4	no	—
254	C₄×C₁₉	—	4	4	no	—
255	C₄×C₁₉	—	4	2	no	—
256	C₄×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
257	C₄×C₁₉	#518	1	1	yes	characteristic
258	C₄×C₁₉	D₄²	1	2	yes	—
259	C₂²×#41	C₂²×C₁₉	1	2	yes	—
260	C₂×#135	—	2	8	no	—
261	C₂×#135	C₄×C₁₉	1	1	yes	characteristic, complemented
262	C₂×#135	C₄×C₁₉	1	2	yes	complemented
263	C₂×#135	C₄×C₁₉	1	1	yes	characteristic, complemented
264	C₂×#135	C₂²×C₁₉	1	2	yes	—
265	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
267	C₂²×Q₁₆	C₄×C₁₉	1	1	yes	characteristic, complemented
268	C₂²×SD₁₆	C₄×C₁₉	1	2	yes	complemented
269	C₂²×D₈	C₄×C₁₉	1	1	yes	characteristic, complemented
270	C₂×#131	C₂²×C₁₉	1	4	yes	complemented
271	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
272	#443	—	2	8	no	—
273	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
274	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
275	C₂×#104	C₂²×C₁₉	1	4	yes	complemented
276	#408	—	2	4	no	—
277	#408	C₂²×C₁₉	1	4	yes	complemented
278	#407	—	2	2	no	—
279	#407	C₂²×C₁₉	1	2	yes	—
280	C₂×C₂²⋊C₈	—	2	2	no	—
281	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂²×C₁₉	1	2	yes	complemented
283	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
284	#341	C₂²×C₁₉	1	2	yes	complemented
285	#336	C₂²×C₁₉	1	2	yes	complemented
286	C₂×C₁₉	—	2	2	no	—
287	C₂×C₁₉	—	2	2	no	—
288	C₂×C₁₉	—	4	1	no	—
289	C₂×C₁₉	—	4	4	no	—
290	C₂×C₁₉	—	8	2	no	—
291	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₁₉	C₂×#443	1	1	yes	characteristic
293	C₂×C₁₉	#2957	1	1	yes	characteristic
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	8	no	—
297	C₂×#41	—	4	4	no	—
298	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
299	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
300	C₂×#41	C₂³×C₁₉	1	2	yes	—
301	C₂×#41	C₂³×C₁₉	1	2	yes	—
302	C₂²×Q₈	C₂×C₄×C₁₉	1	2	yes	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
305	C₂³×C₄	—	2	2	no	—
306	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
307	#135	—	2	8	no	—
308	#135	—	2	4	no	—
309	#135	—	2	8	no	—
310	#135	—	2	4	no	—
311	#135	—	2	4	no	—
312	#135	D₄×C₁₉	1	8	yes	—
313	C₂×Q₁₆	—	2	4	no	—
314	C₂×Q₁₆	C₂×C₄×C₁₉	1	2	yes	—
315	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
316	C₂×Q₁₆	C₂×C₄×C₁₉	1	1	yes	characteristic
317	C₂×SD₁₆	—	2	8	no	—
318	C₂×SD₁₆	C₂×C₄×C₁₉	1	2	yes	—
319	C₂×SD₁₆	C₂×C₄×C₁₉	1	2	yes	—
320	C₂×SD₁₆	C₂×C₄×C₁₉	1	2	yes	—
321	C₂×SD₁₆	C₂×C₄×C₁₉	1	2	yes	—
322	C₂×D₈	—	2	4	no	—
323	C₂×D₈	C₂×C₄×C₁₉	1	2	yes	—
324	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
325	C₂×D₈	C₂×C₄×C₁₉	1	1	yes	characteristic
326	#131	—	2	8	no	—
327	#131	—	4	4	no	—
328	C₂×M₁₆	—	2	4	no	—
329	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
330	C₂²×C₈	—	2	4	no	—
331	C₂²×C₈	—	2	4	no	—
332	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
333	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
338	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
341	#108	—	2	4	no	—
342	#104	—	2	8	no	—
343	#104	—	4	4	no	—
344	C₂²⋊C₈	—	2	2	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	2	4	no	—
347	C₂²⋊C₈	—	2	4	no	—
348	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
349	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
350	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
351	C₄×C₈	—	2	4	no	—
352	#95	—	2	1	no	—
353	C₁₉	#22454	1	1	yes	characteristic, direct product factor, Sylow
354	C₂⁴	—	2	2	no	—
355	C₂⁴	#41×C₁₉	1	1	yes	characteristic
356	#41	—	2	4	no	—
357	#41	—	2	4	no	—
358	#41	—	2	4	no	—
359	#41	—	2	4	no	—
360	#41	—	2	4	no	—
361	#41	—	4	8	no	—
362	#41	—	4	2	no	—
363	#41	—	4	2	no	—
364	#41	—	4	8	no	—
365	#41	C₂×D₄×C₁₉	1	8	yes	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	4	2	no	—
369	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
370	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	8	no	—
379	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
380	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	4	8	no	—
390	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
396	Q₁₆	—	2	4	no	—
397	Q₁₆	—	2	2	no	—
398	Q₁₆	C₂²⋊C₄×C₁₉	1	4	yes	complemented
399	SD₁₆	—	2	4	no	—
400	SD₁₆	—	2	4	no	—
401	SD₁₆	—	2	4	no	—
402	SD₁₆	C₂²⋊C₄×C₁₉	1	8	yes	complemented
403	D₈	—	2	4	no	—
404	D₈	—	2	2	no	—
405	D₈	C₂²⋊C₄×C₁₉	1	4	yes	complemented
406	M₁₆	—	2	4	no	—
407	M₁₆	—	2	4	no	—
408	M₁₆	—	4	8	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	4	no	—
417	C₂×C₈	—	4	8	no	—
418	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
419	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
420	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
421	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
422	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
423	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
424	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	4	no	—
434	C₂³	—	4	4	no	—
435	C₂³	—	8	2	no	—
436	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
437	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
438	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
439	Q₈	—	2	2	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	2	2	no	—
442	Q₈	—	4	4	no	—
443	Q₈	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
444	D₄	—	2	8	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	—	4	4	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	4	no	—
451	D₄	—	4	4	no	—
452	D₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
471	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
472	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
475	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
476	C₈	—	2	1	no	—
477	C₈	—	2	1	no	—
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	—	4	4	no	—
481	C₈	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
482	C₈	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	8	8	no	—
498	C₂²	C₁₉×#443	1	2	yes	complemented
499	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
500	C₂²	C₁₉×#546	1	2	yes	—
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	4	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	2	no	—
506	C₄	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
507	C₄	C₁₉×#518	1	1	yes	characteristic
508	C₄	D₄²×C₁₉	1	2	yes	—
509	C₂	—	2	2	no	—
510	C₂	—	2	2	no	—
511	C₂	—	4	1	no	—
512	C₂	—	4	4	no	—
513	C₂	—	8	2	no	—
514	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
515	C₂	C₂×C₁₉×#443	1	1	yes	characteristic
516	C₂	C₁₉×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×C₄×D₄
prime radical	C₂²×C₁₉×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#443	C₂	semidirect
3. C₁₉×#2880	C₂	semidirect
4. C₁₉×#1974	C₂	semidirect
5. C₁₉×#1876	C₂	semidirect
6. C₁₉×#1810	C₂	semidirect
7. C₁₉×#1789	C₂	semidirect
8. C₈×C₂²⋊C₄×C₁₉	C₂	semidirect
11. C₂×C₁₉×#135	C₄	semidirect
12. C₂×C₁₉×#135	C₄	semidirect
13. C₂×C₁₉×#135	C₄	semidirect
17. C₂²×Q₁₆×C₁₉	C₄	semidirect
18. C₂²×SD₁₆×C₁₉	C₄	semidirect
19. C₂²×D₈×C₁₉	C₄	semidirect
20. C₂×C₁₉×#131	C₂²	semidirect
23. C₂×C₁₉×#108	C₂²	semidirect
24. C₂×C₁₉×#104	C₂²	semidirect
25. C₂×C₁₉×#104	C₂²	semidirect
27. C₁₉×#408	C₂²	semidirect
32. C₂×C₄×C₈×C₁₉	C₂²	semidirect
34. C₁₉×#341	C₂²	semidirect
35. C₁₉×#336	C₂²	semidirect
139. Q₁₆×C₁₉	C₂²⋊C₄	semidirect
143. SD₁₆×C₁₉	C₂²⋊C₄	semidirect
146. D₈×C₁₉	C₂²⋊C₄	semidirect
169. #22454	C₁₉	direct (N × H)
226. C₂×#443	C₂×C₁₉	semidirect
227. #2880	C₂×C₁₉	semidirect
228. #1974	C₂×C₁₉	semidirect
229. #1876	C₂×C₁₉	semidirect
230. #1810	C₂×C₁₉	semidirect
231. #1789	C₂×C₁₉	semidirect
232. C₈×C₂²⋊C₄	C₂×C₁₉	semidirect
248. C₂²×C₁₉	#443	semidirect
261. C₂×#135	C₄×C₁₉	semidirect
262. C₂×#135	C₄×C₁₉	semidirect
263. C₂×#135	C₄×C₁₉	semidirect
267. C₂²×Q₁₆	C₄×C₁₉	semidirect
268. C₂²×SD₁₆	C₄×C₁₉	semidirect
269. C₂²×D₈	C₄×C₁₉	semidirect
270. C₂×#131	C₂²×C₁₉	semidirect
273. C₂×#108	C₂²×C₁₉	semidirect
274. C₂×#104	C₂²×C₁₉	semidirect
275. C₂×#104	C₂²×C₁₉	semidirect
277. #408	C₂²×C₁₉	semidirect
282. C₂×C₄×C₈	C₂²×C₁₉	semidirect
284. #341	C₂²×C₁₉	semidirect
285. #336	C₂²×C₁₉	semidirect
353. C₁₉	#22454	direct (N × H)
398. Q₁₆	C₂²⋊C₄×C₁₉	semidirect
402. SD₁₆	C₂²⋊C₄×C₁₉	semidirect
405. D₈	C₂²⋊C₄×C₁₉	semidirect
498. C₂²	C₁₉×#443	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₉×#135	2
C₂×C₁₉×#443	2
C₁₉×#2880	2
C₁₉×#1974	2
C₁₉×#1876	2
C₁₉×#1810	2
C₁₉×#1789	2
C₈×C₂²⋊C₄×C₁₉	2
#22454	19

Subgroups — C19×#22454 #18028413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#22454 #18028413