Subgroups — C₁₉×#25961 #18031920

Order 4864.

958 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#416	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2341	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2067	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2025	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1863	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1854	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1808	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1788	C₂	1	1	yes	maximal, characteristic
16	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
22	C₁₉×#479	—	2	4	no	—
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₉×#416	—	2	4	no	—
30	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₉×#399	—	2	1	no	—
40	C₁₉×#396	—	2	1	no	—
41	C₁₉×#390	—	2	1	no	—
42	C₁₉×#390	—	2	1	no	—
43	C₁₉×#390	C₂²	1	1	yes	characteristic
44	C₁₉×#390	C₂²	1	1	yes	characteristic
45	C₁₉×#389	—	2	1	no	—
46	C₁₉×#389	C₂²	1	1	yes	characteristic
47	C₁₉×#389	C₂²	1	1	yes	characteristic
48	C₁₉×#387	—	2	1	no	—
49	C₁₉×#384	C₂²	1	1	yes	characteristic
50	C₁₉×#380	—	2	1	no	—
51	C₁₉×#380	C₂²	1	1	yes	characteristic
52	C₁₉×#380	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#340	C₂²	1	1	yes	characteristic
58	C₁₉×#340	C₂²	1	1	yes	characteristic
59	C₁₉×#336	C₂²	1	1	yes	characteristic
60	C₁₉×#336	C₂²	1	1	yes	characteristic
61	C₂×#41×C₁₉	—	2	2	no	—
62	C₂×#41×C₁₉	—	2	2	no	—
63	C₂×#41×C₁₉	—	2	2	no	—
64	C₂×#41×C₁₉	—	4	1	no	—
65	C₂×#41×C₁₉	—	4	1	no	—
66	C₂×#41×C₁₉	Q₈	1	4	yes	—
67	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₉	—	2	1	no	—
69	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₉	—	2	1	no	—
71	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	—	2	2	no	—
73	C₂²×C₈×C₁₉	—	2	2	no	—
74	C₂²×C₈×C₁₉	—	4	1	no	—
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#125	—	2	2	no	—
80	C₁₉×#125	—	4	1	no	—
81	C₄×Q₈×C₁₉	—	2	2	no	—
82	C₄×Q₈×C₁₉	—	2	2	no	—
83	C₄×Q₈×C₁₉	—	4	1	no	—
84	C₄×Q₈×C₁₉	—	4	1	no	—
85	C₁₉×#117	—	2	2	no	—
86	C₁₉×#117	—	4	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₉	—	2	1	no	—
111	C₂×C₄²×C₁₉	—	2	1	no	—
112	C₂×C₄²×C₁₉	—	2	1	no	—
113	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₁₉×#107	—	2	2	no	—
116	C₁₉×#107	—	4	1	no	—
117	C₁₉×#107	—	4	1	no	—
118	C₁₉×#106	—	2	2	no	—
119	C₁₉×C₄⋊C₈	—	2	2	no	—
120	C₁₉×C₄⋊C₈	—	4	1	no	—
121	C₁₉×#103	—	2	2	no	—
122	C₁₉×#103	—	2	2	no	—
123	C₁₉×#103	—	2	2	no	—
124	C₁₉×#103	D₄	1	4	yes	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×#102	—	2	2	no	—
127	C₁₉×#102	—	4	1	no	—
128	C₁₉×#102	—	4	1	no	—
129	C₁₉×C₂²⋊C₈	—	2	2	no	—
130	C₁₉×#95	—	2	1	no	—
131	C₁₉×#95	—	2	1	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	D₄	1	1	yes	characteristic
135	C₁₉×#95	D₄	1	1	yes	characteristic
136	C₂⁴×C₁₉	—	2	1	no	—
137	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
138	#41×C₁₉	—	2	8	no	—
139	#41×C₁₉	—	4	4	no	—
140	#41×C₁₉	—	4	4	no	—
141	#41×C₁₉	—	4	4	no	—
142	C₂×Q₈×C₁₉	—	2	1	no	—
143	C₂×Q₈×C₁₉	—	2	1	no	—
144	C₂×Q₈×C₁₉	—	2	1	no	—
145	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₂×Q₈×C₁₉	C₂×Q₈	1	2	yes	—
147	C₂×Q₈×C₁₉	#41	1	2	yes	—
148	C₂×D₄×C₁₉	—	2	4	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	2	1	no	—
151	C₂×D₄×C₁₉	—	2	1	no	—
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	—	2	1	no	—
154	C₂×D₄×C₁₉	—	4	2	no	—
155	C₂×D₄×C₁₉	—	4	2	no	—
156	C₂×D₄×C₁₉	C₂×Q₈	1	2	yes	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	1	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	1	no	—
161	C₂²×C₄×C₁₉	—	2	1	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	4	no	—
164	C₂²×C₄×C₁₉	—	2	1	no	—
165	C₂²×C₄×C₁₉	—	2	1	no	—
166	C₂²×C₄×C₁₉	—	2	1	no	—
167	C₂²×C₄×C₁₉	—	2	1	no	—
168	C₂²×C₄×C₁₉	—	2	1	no	—
169	C₂²×C₄×C₁₉	—	4	2	no	—
170	C₂²×C₄×C₁₉	—	4	2	no	—
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×Q₈	1	2	yes	—
177	C₂²×C₄×C₁₉	#41	1	2	yes	—
178	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
179	C₂×C₈×C₁₉	—	2	1	no	—
180	C₂×C₈×C₁₉	—	2	1	no	—
181	C₂×C₈×C₁₉	—	2	1	no	—
182	C₂×C₈×C₁₉	—	2	1	no	—
183	C₂×C₈×C₁₉	—	2	1	no	—
184	C₂×C₈×C₁₉	—	2	1	no	—
185	C₂×C₈×C₁₉	—	2	1	no	—
186	C₂×C₈×C₁₉	—	2	1	no	—
187	C₂×C₈×C₁₉	—	2	1	no	—
188	C₂×C₈×C₁₉	—	2	1	no	—
189	C₂×C₈×C₁₉	—	2	1	no	—
190	C₂×C₈×C₁₉	—	4	4	no	—
191	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	2	1	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	1	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	4	2	no	—
204	C₄⋊C₄×C₁₉	—	4	2	no	—
205	C₄⋊C₄×C₁₉	—	4	2	no	—
206	C₄⋊C₄×C₁₉	—	4	2	no	—
207	C₄⋊C₄×C₁₉	—	4	2	no	—
208	C₄⋊C₄×C₁₉	—	4	2	no	—
209	C₄⋊C₄×C₁₉	—	8	1	no	—
210	C₄⋊C₄×C₁₉	—	8	1	no	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	4	1	no	—
214	C₂²⋊C₄×C₁₉	—	4	2	no	—
215	C₂²⋊C₄×C₁₉	—	4	2	no	—
216	C₂²⋊C₄×C₁₉	—	4	2	no	—
217	C₂²⋊C₄×C₁₉	—	8	1	no	—
218	C₂²⋊C₄×C₁₉	—	8	1	no	—
219	C₂²⋊C₄×C₁₉	—	8	1	no	—
220	C₂²⋊C₄×C₁₉	—	8	1	no	—
221	C₄²×C₁₉	—	2	1	no	—
222	C₄²×C₁₉	—	2	1	no	—
223	C₄²×C₁₉	—	2	1	no	—
224	C₄²×C₁₉	—	2	1	no	—
225	C₄²×C₁₉	—	4	2	no	—
226	C₄²×C₁₉	—	4	2	no	—
227	C₄²×C₁₉	—	4	2	no	—
228	#25961	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂³×C₁₉	—	2	1	no	—
230	C₂³×C₁₉	—	2	1	no	—
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	2	1	no	—
233	C₂³×C₁₉	—	2	1	no	—
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	2	2	no	—
236	C₂³×C₁₉	—	4	1	no	—
237	C₂³×C₁₉	—	4	1	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	C₂²⋊Q₈	1	2	yes	—
243	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₁₉	—	2	2	no	—
245	Q₈×C₁₉	—	2	2	no	—
246	Q₈×C₁₉	—	2	2	no	—
247	Q₈×C₁₉	C₂²⋊Q₈	1	4	yes	—
248	D₄×C₁₉	—	2	2	no	—
249	D₄×C₁₉	—	2	2	no	—
250	D₄×C₁₉	—	4	8	no	—
251	D₄×C₁₉	—	4	1	no	—
252	D₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	2	2	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	2	1	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	1	no	—
259	C₂×C₄×C₁₉	—	2	1	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	1	no	—
265	C₂×C₄×C₁₉	—	2	1	no	—
266	C₂×C₄×C₁₉	—	2	2	no	—
267	C₂×C₄×C₁₉	—	2	1	no	—
268	C₂×C₄×C₁₉	—	2	1	no	—
269	C₂×C₄×C₁₉	—	2	1	no	—
270	C₂×C₄×C₁₉	—	2	1	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	1	no	—
273	C₂×C₄×C₁₉	—	2	1	no	—
274	C₂×C₄×C₁₉	—	4	8	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	1	no	—
278	C₂×C₄×C₁₉	—	4	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	1	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	4	1	no	—
285	C₂×C₄×C₁₉	—	4	1	no	—
286	C₂×C₄×C₁₉	—	4	1	no	—
287	C₂×C₄×C₁₉	—	4	1	no	—
288	C₂×C₄×C₁₉	—	4	1	no	—
289	C₂×C₄×C₁₉	—	4	1	no	—
290	C₂×C₄×C₁₉	—	4	1	no	—
291	C₂×C₄×C₁₉	—	4	1	no	—
292	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
293	C₂×C₄×C₁₉	#135	1	2	yes	—
294	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₉	C₂²×Q₈	1	1	yes	characteristic
296	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
300	C₈×C₁₉	—	2	2	no	—
301	C₈×C₁₉	—	4	1	no	—
302	C₈×C₁₉	—	4	1	no	—
303	C₈×C₁₉	—	4	1	no	—
304	C₂×#479	C₂×C₁₉	1	1	yes	characteristic, complemented
305	C₂×#416	C₂×C₁₉	1	1	yes	characteristic
306	#2441	C₂×C₁₉	1	1	yes	characteristic, complemented
307	#2341	C₂×C₁₉	1	1	yes	characteristic
308	#2093	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#2067	C₂×C₁₉	1	1	yes	characteristic, complemented
310	#2065	C₂×C₁₉	1	1	yes	characteristic, complemented
311	#2025	C₂×C₁₉	1	1	yes	characteristic, complemented
312	#1863	C₂×C₁₉	1	1	yes	characteristic, complemented
313	#1863	C₂×C₁₉	1	1	yes	characteristic, complemented
314	#1854	C₂×C₁₉	1	1	yes	characteristic, complemented
315	#1850	C₂×C₁₉	1	1	yes	characteristic, complemented
316	#1808	C₂×C₁₉	1	1	yes	characteristic, complemented
317	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
318	#1788	C₂×C₁₉	1	1	yes	characteristic
319	C₂²×C₁₉	—	2	2	no	—
320	C₂²×C₁₉	—	2	2	no	—
321	C₂²×C₁₉	—	2	2	no	—
322	C₂²×C₁₉	—	4	1	no	—
323	C₂²×C₁₉	—	4	1	no	—
324	C₂²×C₁₉	—	4	1	no	—
325	C₂²×C₁₉	—	4	1	no	—
326	C₂²×C₁₉	—	4	2	no	—
327	C₂²×C₁₉	—	4	2	no	—
328	C₂²×C₁₉	—	4	2	no	—
329	C₂²×C₁₉	—	8	1	no	—
330	C₂²×C₁₉	—	8	1	no	—
331	C₂²×C₁₉	—	8	1	no	—
332	C₂²×C₁₉	—	8	1	no	—
333	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
334	C₂²×C₁₉	D₄²	1	1	yes	characteristic
335	C₂²×C₁₉	#546	1	1	yes	characteristic
336	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
337	C₂²×C₁₉	#575	1	1	yes	characteristic
338	C₂²×C₁₉	#576	1	1	yes	characteristic
339	C₂²×C₁₉	#578	1	1	yes	characteristic
340	C₄×C₁₉	—	2	2	no	—
341	C₄×C₁₉	—	2	4	no	—
342	C₄×C₁₉	—	2	2	no	—
343	C₄×C₁₉	—	4	1	no	—
344	C₄×C₁₉	—	4	2	no	—
345	C₄×C₁₉	—	4	1	no	—
346	C₄×C₁₉	—	4	1	no	—
347	C₄×C₁₉	—	8	1	no	—
348	C₄×C₁₉	—	8	1	no	—
349	C₄×C₁₉	—	8	1	no	—
350	C₄×C₁₉	—	8	1	no	—
351	C₄×C₁₉	—	8	1	no	—
352	C₄×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
353	C₄×C₁₉	#543	1	1	yes	characteristic
354	C₄×C₁₉	#546	1	1	yes	characteristic
355	C₄×C₁₉	#551	1	1	yes	characteristic
356	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
357	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
358	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
359	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
361	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
362	#479	—	2	4	no	—
363	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
364	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
365	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
366	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
368	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
369	#416	—	2	4	no	—
370	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
371	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
372	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
373	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
374	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
375	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
376	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
377	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
378	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
379	#399	—	2	1	no	—
380	#396	—	2	1	no	—
381	#390	—	2	1	no	—
382	#390	—	2	1	no	—
383	#390	C₂²×C₁₉	1	1	yes	characteristic
384	#390	C₂²×C₁₉	1	1	yes	characteristic
385	#389	—	2	1	no	—
386	#389	C₂²×C₁₉	1	1	yes	characteristic
387	#389	C₂²×C₁₉	1	1	yes	characteristic
388	#387	—	2	1	no	—
389	#384	C₂²×C₁₉	1	1	yes	characteristic
390	#380	—	2	1	no	—
391	#380	C₂²×C₁₉	1	1	yes	characteristic
392	#380	C₂²×C₁₉	1	1	yes	characteristic
393	C₄×C₂²⋊C₄	—	2	1	no	—
394	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
395	#340	C₂²×C₁₉	1	1	yes	characteristic
396	#340	C₂²×C₁₉	1	1	yes	characteristic
397	#340	C₂²×C₁₉	1	1	yes	characteristic
398	#340	C₂²×C₁₉	1	1	yes	characteristic
399	#336	C₂²×C₁₉	1	1	yes	characteristic
400	#336	C₂²×C₁₉	1	1	yes	characteristic
401	C₂×C₁₉	—	4	2	no	—
402	C₂×C₁₉	—	8	2	no	—
403	C₂×C₁₉	#2437	1	1	yes	characteristic
404	C₂×C₁₉	#3076	1	1	yes	characteristic
405	C₂×C₁₉	#3083	1	1	yes	characteristic
406	C₂×C₁₉	#3269	1	1	yes	characteristic
407	C₂×C₁₉	#3287	1	1	yes	characteristic
408	C₂×C₁₉	#3300	1	1	yes	characteristic
409	C₂×C₁₉	#3309	1	1	yes	characteristic
410	C₂×#41	—	2	2	no	—
411	C₂×#41	—	2	2	no	—
412	C₂×#41	—	2	2	no	—
413	C₂×#41	—	4	1	no	—
414	C₂×#41	—	4	1	no	—
415	C₂×#41	Q₈×C₁₉	1	4	yes	—
416	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
419	C₂³×C₄	—	2	1	no	—
420	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
421	C₂²×C₈	—	2	2	no	—
422	C₂²×C₈	—	2	2	no	—
423	C₂²×C₈	—	4	1	no	—
424	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
425	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
426	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
428	#125	—	2	2	no	—
429	#125	—	4	1	no	—
430	C₄×Q₈	—	2	2	no	—
431	C₄×Q₈	—	2	2	no	—
432	C₄×Q₈	—	4	1	no	—
433	C₄×Q₈	—	4	1	no	—
434	#117	—	2	2	no	—
435	#117	—	4	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	2	1	no	—
440	C₂×C₄⋊C₄	—	2	1	no	—
441	C₂×C₄⋊C₄	—	2	1	no	—
442	C₂×C₄⋊C₄	—	2	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	—	2	1	no	—
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
459	C₂×C₄²	—	2	1	no	—
460	C₂×C₄²	—	2	1	no	—
461	C₂×C₄²	—	2	1	no	—
462	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
464	#107	—	2	2	no	—
465	#107	—	4	1	no	—
466	#107	—	4	1	no	—
467	#106	—	2	2	no	—
468	C₄⋊C₈	—	2	2	no	—
469	C₄⋊C₈	—	4	1	no	—
470	#103	—	2	2	no	—
471	#103	—	2	2	no	—
472	#103	—	2	2	no	—
473	#103	D₄×C₁₉	1	4	yes	—
474	#102	—	2	2	no	—
475	#102	—	2	2	no	—
476	#102	—	4	1	no	—
477	#102	—	4	1	no	—
478	C₂²⋊C₈	—	2	2	no	—
479	#95	—	2	1	no	—
480	#95	—	2	1	no	—
481	#95	—	2	1	no	—
482	#95	—	2	1	no	—
483	#95	D₄×C₁₉	1	1	yes	characteristic
484	#95	D₄×C₁₉	1	1	yes	characteristic
485	C₁₉	#25961	1	1	yes	characteristic, direct product factor, Sylow
486	C₂⁴	—	2	1	no	—
487	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
488	#41	—	2	8	no	—
489	#41	—	4	4	no	—
490	#41	—	4	4	no	—
491	#41	—	4	4	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
496	C₂×Q₈	C₂×Q₈×C₁₉	1	2	yes	—
497	C₂×Q₈	#41×C₁₉	1	2	yes	—
498	C₂×D₄	—	2	4	no	—
499	C₂×D₄	—	2	1	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	4	2	no	—
505	C₂×D₄	—	4	2	no	—
506	C₂×D₄	C₂×Q₈×C₁₉	1	2	yes	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	—	4	2	no	—
521	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	C₂²×C₄	C₂×Q₈×C₁₉	1	2	yes	—
527	C₂²×C₄	#41×C₁₉	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	4	4	no	—
541	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	2	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	—	8	1	no	—
560	C₄⋊C₄	—	8	1	no	—
561	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	4	1	no	—
564	C₂²⋊C₄	—	4	2	no	—
565	C₂²⋊C₄	—	4	2	no	—
566	C₂²⋊C₄	—	4	2	no	—
567	C₂²⋊C₄	—	8	1	no	—
568	C₂²⋊C₄	—	8	1	no	—
569	C₂²⋊C₄	—	8	1	no	—
570	C₂²⋊C₄	—	8	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	4	2	no	—
576	C₄²	—	4	2	no	—
577	C₄²	—	4	2	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	4	1	no	—
590	C₂³	—	4	1	no	—
591	C₂³	C₁₉×C₂²⋊Q₈	1	2	yes	—
592	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
593	Q₈	—	2	2	no	—
594	Q₈	—	2	2	no	—
595	Q₈	—	2	2	no	—
596	Q₈	C₁₉×C₂²⋊Q₈	1	4	yes	—
597	D₄	—	2	2	no	—
598	D₄	—	2	2	no	—
599	D₄	—	4	8	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	4	8	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
642	C₂×C₄	C₁₉×#135	1	2	yes	—
643	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
644	C₂×C₄	C₂²×Q₈×C₁₉	1	1	yes	characteristic
645	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
646	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
647	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
648	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
649	C₈	—	2	2	no	—
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₈	—	4	1	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	8	1	no	—
664	C₂²	—	8	1	no	—
665	C₂²	—	8	1	no	—
666	C₂²	—	8	1	no	—
667	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
668	C₂²	D₄²×C₁₉	1	1	yes	characteristic
669	C₂²	C₁₉×#546	1	1	yes	characteristic
670	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
671	C₂²	C₁₉×#575	1	1	yes	characteristic
672	C₂²	C₁₉×#576	1	1	yes	characteristic
673	C₂²	C₁₉×#578	1	1	yes	characteristic
674	C₄	—	2	2	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	8	1	no	—
682	C₄	—	8	1	no	—
683	C₄	—	8	1	no	—
684	C₄	—	8	1	no	—
685	C₄	—	8	1	no	—
686	C₄	C₂×C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
687	C₄	C₁₉×#543	1	1	yes	characteristic
688	C₄	C₁₉×#546	1	1	yes	characteristic
689	C₄	C₁₉×#551	1	1	yes	characteristic
690	C₂	—	4	2	no	—
691	C₂	—	8	2	no	—
692	C₂	C₁₉×#2437	1	1	yes	characteristic
693	C₂	C₁₉×#3076	1	1	yes	characteristic
694	C₂	C₁₉×#3083	1	1	yes	characteristic
695	C₂	C₁₉×#3269	1	1	yes	characteristic
696	C₂	C₁₉×#3287	1	1	yes	characteristic
697	C₂	C₁₉×#3300	1	1	yes	characteristic
698	C₂	C₁₉×#3309	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×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
1. C₂×C₁₉×#479	C₂	semidirect
3. C₁₉×#2441	C₂	semidirect
5. C₁₉×#2093	C₂	semidirect
6. C₁₉×#2067	C₂	semidirect
7. C₁₉×#2065	C₂	semidirect
8. C₁₉×#2025	C₂	semidirect
9. C₁₉×#1863	C₂	semidirect
10. C₁₉×#1863	C₂	semidirect
11. C₁₉×#1854	C₂	semidirect
12. C₁₉×#1850	C₂	semidirect
13. C₁₉×#1808	C₂	semidirect
14. C₁₉×#1803	C₂	semidirect
228. #25961	C₁₉	direct (N × H)
304. C₂×#479	C₂×C₁₉	semidirect
306. #2441	C₂×C₁₉	semidirect
308. #2093	C₂×C₁₉	semidirect
309. #2067	C₂×C₁₉	semidirect
310. #2065	C₂×C₁₉	semidirect
311. #2025	C₂×C₁₉	semidirect
312. #1863	C₂×C₁₉	semidirect
313. #1863	C₂×C₁₉	semidirect
314. #1854	C₂×C₁₉	semidirect
315. #1850	C₂×C₁₉	semidirect
316. #1808	C₂×C₁₉	semidirect
317. #1803	C₂×C₁₉	semidirect
485. C₁₉	#25961	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×#479	2
C₂×C₁₉×#416	2
C₁₉×#2441	2
C₁₉×#2341	2
C₁₉×#2093	2
C₁₉×#2067	2
C₁₉×#2065	2
C₁₉×#2025	2
C₁₉×#1863	2
C₁₉×#1854	2
C₁₉×#1850	2
C₁₉×#1808	2
C₁₉×#1803	2
C₁₉×#1788	2
#25961	19

Subgroups — C19×#25961 #18031920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#25961 #18031920