Subgroups — C₁₉×#29134 #18035093

Order 4864.

690 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2326	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2042	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1936	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1934	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1805	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#1804	C₂	1	1	yes	maximal, characteristic
13	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#1802	C₂	1	1	yes	maximal, characteristic
15	C₁₉×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#400	—	2	1	no	—
32	C₁₉×#400	—	2	1	no	—
33	C₁₉×#398	—	2	1	no	—
34	C₁₉×#398	—	2	1	no	—
35	C₁₉×#391	C₂²	1	1	yes	characteristic
36	C₁₉×#390	C₂²	1	1	yes	characteristic
37	C₁₉×#389	C₂²	1	1	yes	characteristic
38	C₁₉×#389	C₂²	1	1	yes	characteristic
39	C₁₉×#389	C₂²	1	1	yes	characteristic
40	C₁₉×#389	C₂²	1	1	yes	characteristic
41	C₁₉×#388	—	2	1	no	—
42	C₁₉×#388	—	2	1	no	—
43	C₁₉×#385	—	2	1	no	—
44	C₁₉×#385	—	2	1	no	—
45	C₁₉×#384	C₂²	1	1	yes	characteristic
46	C₁₉×#384	C₂²	1	1	yes	characteristic
47	C₁₉×#382	C₂²	1	1	yes	characteristic
48	C₁₉×#376	C₂²	1	1	yes	characteristic
49	C₁₉×#340	C₂²	1	1	yes	characteristic
50	C₁₉×#340	C₂²	1	1	yes	characteristic
51	C₁₉×#340	C₂²	1	1	yes	characteristic
52	C₁₉×#340	C₂²	1	1	yes	characteristic
53	C₁₉×#340	C₂²	1	1	yes	characteristic
54	C₁₉×#340	C₂²	1	1	yes	characteristic
55	C₁₉×#340	C₂²	1	1	yes	characteristic
56	C₁₉×#340	C₂²	1	1	yes	characteristic
57	C₁₉×#336	C₂²	1	1	yes	characteristic
58	C₁₉×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₁₉×#124	—	2	2	no	—
67	C₁₉×#124	—	2	2	no	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄²×C₁₉	—	2	1	no	—
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
96	C₁₉×C₄⋊C₈	—	2	2	no	—
97	C₁₉×C₄⋊C₈	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	4	1	no	—
101	C₁₉×#103	—	4	1	no	—
102	C₁₉×#102	—	2	2	no	—
103	C₁₉×#102	—	2	2	no	—
104	C₁₉×#102	—	4	1	no	—
105	C₁₉×#102	—	4	1	no	—
106	C₁₉×#97	—	4	1	no	—
107	C₄×C₈×C₁₉	—	4	1	no	—
108	C₁₉×#95	—	2	1	no	—
109	C₁₉×#95	—	2	1	no	—
110	C₁₉×#95	—	2	1	no	—
111	C₁₉×#95	—	2	1	no	—
112	C₁₉×#95	—	2	1	no	—
113	C₁₉×#95	—	2	1	no	—
114	C₁₉×#95	—	2	1	no	—
115	C₁₉×#95	—	2	1	no	—
116	C₁₉×#95	D₄	1	1	yes	characteristic
117	C₁₉×#95	D₄	1	1	yes	characteristic
118	C₁₉×#95	D₄	1	1	yes	characteristic
119	C₁₉×#95	D₄	1	1	yes	characteristic
120	C₂⁴×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	#41	1	2	yes	—
127	C₂×D₄×C₁₉	—	2	1	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	2	1	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	#41	1	2	yes	—
133	C₂²×C₄×C₁₉	—	2	1	no	—
134	C₂²×C₄×C₁₉	—	2	1	no	—
135	C₂²×C₄×C₁₉	—	2	1	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	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	4	2	no	—
141	C₂²×C₄×C₁₉	—	8	1	no	—
142	C₂²×C₄×C₁₉	—	8	1	no	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	2	1	no	—
157	C₂×C₈×C₁₉	—	2	1	no	—
158	C₂×C₈×C₁₉	—	2	1	no	—
159	C₂×C₈×C₁₉	—	2	1	no	—
160	C₂×C₈×C₁₉	—	2	1	no	—
161	C₂×C₈×C₁₉	—	2	1	no	—
162	C₄⋊C₄×C₁₉	—	2	1	no	—
163	C₄⋊C₄×C₁₉	—	2	1	no	—
164	C₄⋊C₄×C₁₉	—	2	1	no	—
165	C₄⋊C₄×C₁₉	—	2	1	no	—
166	C₄⋊C₄×C₁₉	—	2	1	no	—
167	C₄⋊C₄×C₁₉	—	2	1	no	—
168	C₄⋊C₄×C₁₉	—	2	1	no	—
169	C₄⋊C₄×C₁₉	—	2	1	no	—
170	C₄⋊C₄×C₁₉	—	2	1	no	—
171	C₄⋊C₄×C₁₉	—	2	1	no	—
172	C₄⋊C₄×C₁₉	—	2	1	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	4	2	no	—
175	C₄⋊C₄×C₁₉	—	8	1	no	—
176	C₄⋊C₄×C₁₉	—	8	1	no	—
177	C₄⋊C₄×C₁₉	—	8	1	no	—
178	C₄⋊C₄×C₁₉	—	8	1	no	—
179	C₄⋊C₄×C₁₉	—	8	1	no	—
180	C₄⋊C₄×C₁₉	—	8	1	no	—
181	C₄⋊C₄×C₁₉	—	8	1	no	—
182	C₄⋊C₄×C₁₉	—	8	1	no	—
183	C₂²⋊C₄×C₁₉	—	2	4	no	—
184	C₂²⋊C₄×C₁₉	—	2	4	no	—
185	C₂²⋊C₄×C₁₉	—	4	2	no	—
186	C₂²⋊C₄×C₁₉	—	8	1	no	—
187	C₂²⋊C₄×C₁₉	—	8	1	no	—
188	C₄²×C₁₉	—	2	1	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	4	2	no	—
193	C₄²×C₁₉	#41	1	2	yes	—
194	C₄²×C₁₉	#41	1	2	yes	—
195	#29134	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	1	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	1	no	—
201	C₂³×C₁₉	—	4	1	no	—
202	C₂³×C₁₉	—	4	1	no	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₉	—	2	2	no	—
205	Q₈×C₁₉	—	2	2	no	—
206	Q₈×C₁₉	—	4	1	no	—
207	Q₈×C₁₉	—	4	1	no	—
208	D₄×C₁₉	—	2	2	no	—
209	D₄×C₁₉	—	2	2	no	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	2	1	no	—
213	C₂×C₄×C₁₉	—	2	1	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	1	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	1	no	—
221	C₂×C₄×C₁₉	—	2	1	no	—
222	C₂×C₄×C₁₉	—	2	1	no	—
223	C₂×C₄×C₁₉	—	2	1	no	—
224	C₂×C₄×C₁₉	—	2	1	no	—
225	C₂×C₄×C₁₉	—	2	1	no	—
226	C₂×C₄×C₁₉	—	2	1	no	—
227	C₂×C₄×C₁₉	—	2	1	no	—
228	C₂×C₄×C₁₉	—	2	1	no	—
229	C₂×C₄×C₁₉	—	4	1	no	—
230	C₂×C₄×C₁₉	—	4	1	no	—
231	C₂×C₄×C₁₉	—	4	1	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	4	1	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	1	no	—
237	C₂×C₄×C₁₉	—	4	1	no	—
238	C₂×C₄×C₁₉	—	4	1	no	—
239	C₂×C₄×C₁₉	—	4	1	no	—
240	C₂×C₄×C₁₉	—	4	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	1	no	—
243	C₂×C₄×C₁₉	—	4	1	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	1	no	—
247	C₂×C₄×C₁₉	—	4	1	no	—
248	C₂×C₄×C₁₉	—	4	1	no	—
249	C₂×C₄×C₁₉	—	8	4	no	—
250	C₂×C₄×C₁₉	#124	1	2	yes	—
251	C₂×C₄×C₁₉	#124	1	2	yes	—
252	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
258	C₈×C₁₉	—	4	1	no	—
259	C₈×C₁₉	—	4	1	no	—
260	C₈×C₁₉	—	4	1	no	—
261	C₈×C₁₉	—	4	1	no	—
262	#2647	C₂×C₁₉	1	1	yes	characteristic, complemented
263	#2326	C₂×C₁₉	1	1	yes	characteristic
264	#2100	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#2099	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#2042	C₂×C₁₉	1	1	yes	characteristic
267	#2042	C₂×C₁₉	1	1	yes	characteristic
268	#1936	C₂×C₁₉	1	1	yes	characteristic
269	#1935	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1934	C₂×C₁₉	1	1	yes	characteristic
271	#1933	C₂×C₁₉	1	1	yes	characteristic, complemented
272	#1805	C₂×C₁₉	1	1	yes	characteristic, complemented
273	#1804	C₂×C₁₉	1	1	yes	characteristic
274	#1803	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1802	C₂×C₁₉	1	1	yes	characteristic
276	#1768	C₂×C₁₉	1	1	yes	characteristic, complemented
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	2	no	—
279	C₂²×C₁₉	—	4	2	no	—
280	C₂²×C₁₉	—	8	1	no	—
281	C₂²×C₁₉	—	8	1	no	—
282	C₂²×C₁₉	—	8	1	no	—
283	C₂²×C₁₉	—	8	1	no	—
284	C₂²×C₁₉	#525	1	1	yes	characteristic
285	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
286	C₂²×C₁₉	#537	1	1	yes	characteristic
287	C₂²×C₁₉	#576	1	1	yes	characteristic
288	C₂²×C₁₉	#577	1	1	yes	characteristic
289	C₂²×C₁₉	#577	1	1	yes	characteristic
290	C₂²×C₁₉	#578	1	1	yes	characteristic
291	C₄×C₁₉	—	2	2	no	—
292	C₄×C₁₉	—	2	2	no	—
293	C₄×C₁₉	—	4	2	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	4	1	no	—
296	C₄×C₁₉	—	4	1	no	—
297	C₄×C₁₉	—	4	1	no	—
298	C₄×C₁₉	—	8	1	no	—
299	C₄×C₁₉	—	8	1	no	—
300	C₄×C₁₉	—	8	1	no	—
301	C₄×C₁₉	—	8	1	no	—
302	C₄×C₁₉	—	8	1	no	—
303	C₄×C₁₉	—	8	1	no	—
304	C₄×C₁₉	#552	1	1	yes	characteristic
305	C₄×C₁₉	#552	1	1	yes	characteristic
306	C₄×C₁₉	#553	1	1	yes	characteristic
307	C₄×C₁₉	#553	1	1	yes	characteristic
308	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
310	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
311	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
313	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
314	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
318	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
319	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
320	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
321	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
322	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
323	#400	—	2	1	no	—
324	#400	—	2	1	no	—
325	#398	—	2	1	no	—
326	#398	—	2	1	no	—
327	#391	C₂²×C₁₉	1	1	yes	characteristic
328	#390	C₂²×C₁₉	1	1	yes	characteristic
329	#389	C₂²×C₁₉	1	1	yes	characteristic
330	#389	C₂²×C₁₉	1	1	yes	characteristic
331	#389	C₂²×C₁₉	1	1	yes	characteristic
332	#389	C₂²×C₁₉	1	1	yes	characteristic
333	#388	—	2	1	no	—
334	#388	—	2	1	no	—
335	#385	—	2	1	no	—
336	#385	—	2	1	no	—
337	#384	C₂²×C₁₉	1	1	yes	characteristic
338	#384	C₂²×C₁₉	1	1	yes	characteristic
339	#382	C₂²×C₁₉	1	1	yes	characteristic
340	#376	C₂²×C₁₉	1	1	yes	characteristic
341	#340	C₂²×C₁₉	1	1	yes	characteristic
342	#340	C₂²×C₁₉	1	1	yes	characteristic
343	#340	C₂²×C₁₉	1	1	yes	characteristic
344	#340	C₂²×C₁₉	1	1	yes	characteristic
345	#340	C₂²×C₁₉	1	1	yes	characteristic
346	#340	C₂²×C₁₉	1	1	yes	characteristic
347	#340	C₂²×C₁₉	1	1	yes	characteristic
348	#340	C₂²×C₁₉	1	1	yes	characteristic
349	#336	C₂²×C₁₉	1	1	yes	characteristic
350	#336	C₂²×C₁₉	1	1	yes	characteristic
351	C₂×C₁₉	—	8	2	no	—
352	C₂×C₁₉	#2562	1	1	yes	characteristic
353	C₂×C₁₉	#3119	1	1	yes	characteristic
354	C₂×C₁₉	#3120	1	1	yes	characteristic
355	C₂×C₁₉	#3136	1	1	yes	characteristic
356	C₂×C₁₉	#3137	1	1	yes	characteristic
357	C₂×C₁₉	#3262	1	1	yes	characteristic
358	C₂×C₁₉	#3263	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
360	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
363	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
365	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
366	#124	—	2	2	no	—
367	#124	—	2	2	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
396	C₄⋊C₈	—	2	2	no	—
397	C₄⋊C₈	—	2	2	no	—
398	#103	—	2	2	no	—
399	#103	—	2	2	no	—
400	#103	—	4	1	no	—
401	#103	—	4	1	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	4	1	no	—
405	#102	—	4	1	no	—
406	#97	—	4	1	no	—
407	C₄×C₈	—	4	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	D₄×C₁₉	1	1	yes	characteristic
417	#95	D₄×C₁₉	1	1	yes	characteristic
418	#95	D₄×C₁₉	1	1	yes	characteristic
419	#95	D₄×C₁₉	1	1	yes	characteristic
420	C₁₉	#29134	1	1	yes	characteristic, direct product factor, Sylow
421	C₂⁴	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	#41×C₁₉	1	2	yes	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	#41×C₁₉	1	2	yes	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	—	8	1	no	—
443	C₂²×C₄	—	8	1	no	—
444	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	4	2	no	—
476	C₄⋊C₄	—	8	1	no	—
477	C₄⋊C₄	—	8	1	no	—
478	C₄⋊C₄	—	8	1	no	—
479	C₄⋊C₄	—	8	1	no	—
480	C₄⋊C₄	—	8	1	no	—
481	C₄⋊C₄	—	8	1	no	—
482	C₄⋊C₄	—	8	1	no	—
483	C₄⋊C₄	—	8	1	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	4	2	no	—
487	C₂²⋊C₄	—	8	1	no	—
488	C₂²⋊C₄	—	8	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	4	2	no	—
494	C₄²	#41×C₁₉	1	2	yes	—
495	C₄²	#41×C₁₉	1	2	yes	—
496	C₂³	—	2	2	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	Q₈	—	2	2	no	—
505	Q₈	—	2	2	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	D₄	—	2	2	no	—
509	D₄	—	2	2	no	—
510	D₄	—	4	1	no	—
511	D₄	—	4	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	8	4	no	—
550	C₂×C₄	C₁₉×#124	1	2	yes	—
551	C₂×C₄	C₁₉×#124	1	2	yes	—
552	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
553	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
554	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
555	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
556	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
557	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	C₁₉×#525	1	1	yes	characteristic
570	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
571	C₂²	C₁₉×#537	1	1	yes	characteristic
572	C₂²	C₁₉×#576	1	1	yes	characteristic
573	C₂²	C₁₉×#577	1	1	yes	characteristic
574	C₂²	C₁₉×#577	1	1	yes	characteristic
575	C₂²	C₁₉×#578	1	1	yes	characteristic
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	8	1	no	—
584	C₄	—	8	1	no	—
585	C₄	—	8	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	C₁₉×#552	1	1	yes	characteristic
590	C₄	C₁₉×#552	1	1	yes	characteristic
591	C₄	C₁₉×#553	1	1	yes	characteristic
592	C₄	C₁₉×#553	1	1	yes	characteristic
593	C₂	—	8	2	no	—
594	C₂	C₁₉×#2562	1	1	yes	characteristic
595	C₂	C₁₉×#3119	1	1	yes	characteristic
596	C₂	C₁₉×#3120	1	1	yes	characteristic
597	C₂	C₁₉×#3136	1	1	yes	characteristic
598	C₂	C₁₉×#3137	1	1	yes	characteristic
599	C₂	C₁₉×#3262	1	1	yes	characteristic
600	C₂	C₁₉×#3263	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₁₉×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2647	C₂	semidirect
3. C₁₉×#2100	C₂	semidirect
4. C₁₉×#2099	C₂	semidirect
8. C₁₉×#1935	C₂	semidirect
10. C₁₉×#1933	C₂	semidirect
11. C₁₉×#1805	C₂	semidirect
13. C₁₉×#1803	C₂	semidirect
15. C₁₉×#1768	C₂	semidirect
195. #29134	C₁₉	direct (N × H)
262. #2647	C₂×C₁₉	semidirect
264. #2100	C₂×C₁₉	semidirect
265. #2099	C₂×C₁₉	semidirect
269. #1935	C₂×C₁₉	semidirect
271. #1933	C₂×C₁₉	semidirect
272. #1805	C₂×C₁₉	semidirect
274. #1803	C₂×C₁₉	semidirect
276. #1768	C₂×C₁₉	semidirect
420. C₁₉	#29134	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2647	2
C₁₉×#2326	2
C₁₉×#2100	2
C₁₉×#2099	2
C₁₉×#2042	2
C₁₉×#1936	2
C₁₉×#1935	2
C₁₉×#1934	2
C₁₉×#1933	2
C₁₉×#1805	2
C₁₉×#1804	2
C₁₉×#1803	2
C₁₉×#1802	2
C₁₉×#1768	2
#29134	19

Subgroups — C19×#29134 #18035093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#29134 #18035093