Subgroups — C₁₉×#16253 #18022212

Order 4864.

2570 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#394	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#393	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1441	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1439	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1438	C₂	1	4	yes	maximal, complemented
8	C₁₉×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
14	C₂×C₁₉×C₂²⋊Q₈	—	2	8	no	—
15	C₂×C₁₉×#121	—	2	4	no	—
16	C₂×C₁₉×#121	—	2	8	no	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
25	C₁₉×#394	—	2	8	no	—
26	C₁₉×#393	—	2	8	no	—
27	C₂×C₁₉×#95	C₂²	1	2	yes	—
28	C₂×C₁₉×#95	C₂²	1	2	yes	—
29	C₂×C₁₉×#95	C₂²	1	4	yes	—
30	C₂×C₁₉×#95	C₂²	1	4	yes	—
31	C₂⁵×C₁₉	C₂³	1	2	yes	—
32	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
33	C₂²×Q₈×C₁₉	—	2	4	no	—
34	C₂²×Q₈×C₁₉	—	2	2	no	—
35	C₂²×Q₈×C₁₉	—	2	4	no	—
36	C₂²×Q₈×C₁₉	—	4	2	no	—
37	C₂²×D₄×C₁₉	—	2	4	no	—
38	C₂²×D₄×C₁₉	—	2	4	no	—
39	C₂²×D₄×C₁₉	—	2	4	no	—
40	C₂²×D₄×C₁₉	—	2	8	no	—
41	C₂²×D₄×C₁₉	—	2	4	no	—
42	C₂²×D₄×C₁₉	—	2	2	no	—
43	C₂²×D₄×C₁₉	—	2	4	no	—
44	C₂²×D₄×C₁₉	—	4	2	no	—
45	C₂²×D₄×C₁₉	—	4	4	no	—
46	C₂³×C₄×C₁₉	—	2	4	no	—
47	C₂³×C₄×C₁₉	—	2	4	no	—
48	C₂³×C₄×C₁₉	—	4	2	no	—
49	C₂³×C₄×C₁₉	D₄	1	4	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₁₉×C₂²⋊Q₈	—	2	32	no	—
57	C₁₉×#121	—	2	32	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	complemented
65	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
78	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
79	C₂×C₂²⋊C₄×C₁₉	D₄	1	8	yes	—
80	C₁₉×#95	—	2	8	no	—
81	C₁₉×#95	—	2	4	no	—
82	C₁₉×#95	—	2	4	no	—
83	C₁₉×#95	—	4	4	no	—
84	C₂⁴×C₁₉	—	2	2	no	—
85	C₂⁴×C₁₉	—	2	2	no	—
86	C₂⁴×C₁₉	—	2	1	no	—
87	C₂⁴×C₁₉	—	2	2	no	—
88	C₂⁴×C₁₉	—	2	2	no	—
89	C₂⁴×C₁₉	—	2	2	no	—
90	C₂⁴×C₁₉	—	2	1	no	—
91	C₂⁴×C₁₉	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	2	no	—
93	C₂⁴×C₁₉	—	2	2	no	—
94	C₂⁴×C₁₉	—	2	4	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	—	2	4	no	—
97	C₂⁴×C₁₉	—	2	4	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	—	2	2	no	—
101	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
102	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
103	C₂⁴×C₁₉	#41	1	4	yes	—
104	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
105	C₂×Q₈×C₁₉	—	2	8	no	—
106	C₂×Q₈×C₁₉	—	4	16	no	—
107	C₂×Q₈×C₁₉	—	4	4	no	—
108	C₂×Q₈×C₁₉	—	4	4	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	16	no	—
111	C₂×D₄×C₁₉	—	4	16	no	—
112	C₂×D₄×C₁₉	—	4	16	no	—
113	C₂×D₄×C₁₉	—	4	4	no	—
114	C₂×D₄×C₁₉	—	4	16	no	—
115	C₂×D₄×C₁₉	—	4	8	no	—
116	C₂×D₄×C₁₉	—	4	8	no	—
117	C₂×D₄×C₁₉	—	4	4	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
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	4	no	—
129	C₂²×C₄×C₁₉	—	2	4	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	4	no	—
133	C₂²×C₄×C₁₉	—	2	4	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	8	no	—
137	C₂²×C₄×C₁₉	—	2	8	no	—
138	C₂²×C₄×C₁₉	—	2	4	no	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	4	no	—
142	C₂²×C₄×C₁₉	—	2	4	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	4	4	no	—
146	C₂²×C₄×C₁₉	—	4	16	no	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₁₉	—	2	8	no	—
155	C₄⋊C₄×C₁₉	—	2	8	no	—
156	C₄⋊C₄×C₁₉	—	2	16	no	—
157	C₂²⋊C₄×C₁₉	—	2	16	no	—
158	C₂²⋊C₄×C₁₉	—	2	16	no	—
159	C₂²⋊C₄×C₁₉	—	4	16	no	—
160	C₂²⋊C₄×C₁₉	—	4	16	no	—
161	C₂²⋊C₄×C₁₉	—	4	8	no	—
162	#16253	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	2	no	—
167	C₂³×C₁₉	—	2	2	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	2	4	no	—
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	8	no	—
172	C₂³×C₁₉	—	2	8	no	—
173	C₂³×C₁₉	—	2	4	no	—
174	C₂³×C₁₉	—	2	4	no	—
175	C₂³×C₁₉	—	2	4	no	—
176	C₂³×C₁₉	—	2	8	no	—
177	C₂³×C₁₉	—	2	8	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	—	4	4	no	—
183	C₂³×C₁₉	—	4	4	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	4	no	—
188	C₂³×C₁₉	—	4	2	no	—
189	C₂³×C₁₉	—	4	2	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	4	2	no	—
192	C₂³×C₁₉	—	4	2	no	—
193	C₂³×C₁₉	—	4	4	no	—
194	C₂³×C₁₉	—	4	4	no	—
195	C₂³×C₁₉	—	4	4	no	—
196	C₂³×C₁₉	—	4	4	no	—
197	C₂³×C₁₉	—	4	4	no	—
198	C₂³×C₁₉	—	4	4	no	—
199	C₂³×C₁₉	—	4	4	no	—
200	C₂³×C₁₉	—	4	4	no	—
201	C₂³×C₁₉	—	4	4	no	—
202	C₂³×C₁₉	#124	1	4	yes	—
203	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
205	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
206	C₂³×C₁₉	C₂×#41	1	2	yes	—
207	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
208	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
210	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
211	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
212	Q₈×C₁₉	—	4	16	no	—
213	D₄×C₁₉	—	4	16	no	—
214	D₄×C₁₉	—	4	32	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	2	2	no	—
219	C₂×C₄×C₁₉	—	2	8	no	—
220	C₂×C₄×C₁₉	—	2	8	no	—
221	C₂×C₄×C₁₉	—	2	4	no	—
222	C₂×C₄×C₁₉	—	2	4	no	—
223	C₂×C₄×C₁₉	—	2	4	no	—
224	C₂×C₄×C₁₉	—	2	4	no	—
225	C₂×C₄×C₁₉	—	2	4	no	—
226	C₂×C₄×C₁₉	—	2	8	no	—
227	C₂×C₄×C₁₉	—	2	8	no	—
228	C₂×C₄×C₁₉	—	4	16	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	2	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	2	no	—
235	C₂×C₄×C₁₉	—	4	2	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	4	4	no	—
238	C₂×C₄×C₁₉	—	4	4	no	—
239	C₂×C₄×C₁₉	—	4	4	no	—
240	C₂×C₄×C₁₉	—	4	4	no	—
241	C₂×C₄×C₁₉	—	4	4	no	—
242	C₂×C₄×C₁₉	—	4	4	no	—
243	C₂×C₄×C₁₉	—	4	4	no	—
244	C₂×C₄×C₁₉	—	4	4	no	—
245	C₂×C₄×C₁₉	—	4	4	no	—
246	C₂×C₄×C₁₉	#120	1	4	yes	—
247	C₂×C₄×C₁₉	#120	1	4	yes	—
248	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
249	C₂²×#121	C₂×C₁₉	1	1	yes	characteristic
250	C₂×#394	C₂×C₁₉	1	2	yes	complemented
251	C₂×#393	C₂×C₁₉	1	2	yes	complemented
252	#1441	C₂×C₁₉	1	2	yes	complemented
253	#1439	C₂×C₁₉	1	2	yes	complemented
254	#1438	C₂×C₁₉	1	4	yes	complemented
255	C₂²⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
256	C₂²×C₁₉	—	2	4	no	—
257	C₂²×C₁₉	—	2	4	no	—
258	C₂²×C₁₉	—	2	4	no	—
259	C₂²×C₁₉	—	4	2	no	—
260	C₂²×C₁₉	—	4	2	no	—
261	C₂²×C₁₉	—	4	2	no	—
262	C₂²×C₁₉	—	4	2	no	—
263	C₂²×C₁₉	—	4	8	no	—
264	C₂²×C₁₉	—	4	8	no	—
265	C₂²×C₁₉	—	4	4	no	—
266	C₂²×C₁₉	—	4	4	no	—
267	C₂²×C₁₉	—	4	8	no	—
268	C₂²×C₁₉	—	4	8	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	8	2	no	—
271	C₂²×C₁₉	—	8	2	no	—
272	C₂²×C₁₉	—	8	2	no	—
273	C₂²×C₁₉	—	8	4	no	—
274	C₂²×C₁₉	—	8	4	no	—
275	C₂²×C₁₉	—	8	2	no	—
276	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
277	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
278	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
279	C₂²×C₁₉	#534	1	1	yes	characteristic
280	C₂²×C₁₉	#535	1	1	yes	characteristic
281	C₂²×C₁₉	#535	1	2	yes	—
282	C₂²×C₁₉	#536	1	1	yes	characteristic
283	C₂²×C₁₉	#536	1	2	yes	—
284	C₂²×C₁₉	#537	1	1	yes	characteristic
285	C₂²×C₁₉	#537	1	2	yes	—
286	C₂²×C₁₉	#537	1	2	yes	—
287	C₂²×C₁₉	#538	1	2	yes	—
288	C₂²×C₁₉	#539	1	2	yes	—
289	C₂²×C₁₉	D₄²	1	4	yes	—
290	C₂²×C₁₉	#546	1	4	yes	—
291	C₂²×C₁₉	#548	1	4	yes	—
292	C₂²×C₁₉	#562	1	4	yes	—
293	C₄×C₁₉	—	2	4	no	—
294	C₄×C₁₉	—	2	4	no	—
295	C₄×C₁₉	—	4	4	no	—
296	C₄×C₁₉	—	4	4	no	—
297	C₄×C₁₉	—	4	4	no	—
298	C₄×C₁₉	—	8	4	no	—
299	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
300	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
301	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
302	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×C₂²⋊Q₈	—	2	4	no	—
304	C₂×C₂²⋊Q₈	—	2	8	no	—
305	C₂×#121	—	2	4	no	—
306	C₂×#121	—	2	8	no	—
307	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
308	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
310	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
311	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
312	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
314	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
315	#394	—	2	8	no	—
316	#393	—	2	8	no	—
317	C₂×#95	C₂²×C₁₉	1	2	yes	—
318	C₂×#95	C₂²×C₁₉	1	4	yes	—
319	C₂×#95	C₂²×C₁₉	1	2	yes	—
320	C₂×#95	C₂²×C₁₉	1	4	yes	—
321	C₂×C₁₉	—	4	4	no	—
322	C₂×C₁₉	—	8	4	no	—
323	C₂×C₁₉	#2403	1	1	yes	characteristic
324	C₂×C₁₉	#2435	1	1	yes	characteristic
325	C₂×C₁₉	#2436	1	1	yes	characteristic
326	C₂×C₁₉	#2615	1	1	yes	characteristic
327	C₂×C₁₉	#2616	1	1	yes	characteristic
328	C₂×C₁₉	#2639	1	1	yes	characteristic
329	C₂×C₁₉	#2676	1	4	yes	—
330	C₂×C₁₉	#2681	1	4	yes	—
331	C₂×C₁₉	#2816	1	1	yes	characteristic
332	C₂⁵	C₂³×C₁₉	1	2	yes	—
333	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
334	C₂²×Q₈	—	2	4	no	—
335	C₂²×Q₈	—	2	2	no	—
336	C₂²×Q₈	—	2	4	no	—
337	C₂²×Q₈	—	4	2	no	—
338	C₂²×D₄	—	2	4	no	—
339	C₂²×D₄	—	2	4	no	—
340	C₂²×D₄	—	2	4	no	—
341	C₂²×D₄	—	2	8	no	—
342	C₂²×D₄	—	2	4	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	4	no	—
345	C₂²×D₄	—	4	2	no	—
346	C₂²×D₄	—	4	4	no	—
347	C₂³×C₄	—	2	4	no	—
348	C₂³×C₄	—	2	4	no	—
349	C₂³×C₄	—	4	2	no	—
350	C₂³×C₄	D₄×C₁₉	1	4	yes	—
351	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
352	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
353	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
354	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂²⋊Q₈	—	2	32	no	—
358	#121	—	2	32	no	—
359	C₂×C₄⋊C₄	—	2	4	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	4	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	4	no	—
364	C₂×C₄⋊C₄	—	2	4	no	—
365	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	complemented
366	C₂×C₂²⋊C₄	—	2	4	no	—
367	C₂×C₂²⋊C₄	—	2	4	no	—
368	C₂×C₂²⋊C₄	—	2	4	no	—
369	C₂×C₂²⋊C₄	—	2	4	no	—
370	C₂×C₂²⋊C₄	—	2	4	no	—
371	C₂×C₂²⋊C₄	—	2	8	no	—
372	C₂×C₂²⋊C₄	—	2	4	no	—
373	C₂×C₂²⋊C₄	—	2	8	no	—
374	C₂×C₂²⋊C₄	—	2	8	no	—
375	C₂×C₂²⋊C₄	—	4	4	no	—
376	C₂×C₂²⋊C₄	—	4	4	no	—
377	C₂×C₂²⋊C₄	—	4	4	no	—
378	C₂×C₂²⋊C₄	—	4	2	no	—
379	C₂×C₂²⋊C₄	—	4	2	no	—
380	C₂×C₂²⋊C₄	D₄×C₁₉	1	8	yes	—
381	#95	—	2	8	no	—
382	#95	—	2	4	no	—
383	#95	—	2	4	no	—
384	#95	—	4	4	no	—
385	C₁₉	#16253	1	1	yes	characteristic, direct product factor, Sylow
386	C₂⁴	—	2	2	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	1	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	—	2	1	no	—
393	C₂⁴	—	2	4	no	—
394	C₂⁴	—	2	2	no	—
395	C₂⁴	—	2	2	no	—
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	4	no	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	2	no	—
403	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
404	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
405	C₂⁴	#41×C₁₉	1	4	yes	—
406	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
407	C₂×Q₈	—	2	8	no	—
408	C₂×Q₈	—	4	16	no	—
409	C₂×Q₈	—	4	4	no	—
410	C₂×Q₈	—	4	4	no	—
411	C₂×D₄	—	2	8	no	—
412	C₂×D₄	—	2	16	no	—
413	C₂×D₄	—	4	16	no	—
414	C₂×D₄	—	4	16	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	16	no	—
417	C₂×D₄	—	4	8	no	—
418	C₂×D₄	—	4	8	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	4	4	no	—
448	C₂²×C₄	—	4	16	no	—
449	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
450	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
451	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
452	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
453	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
454	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
455	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	16	no	—
459	C₂²⋊C₄	—	2	16	no	—
460	C₂²⋊C₄	—	2	16	no	—
461	C₂²⋊C₄	—	4	16	no	—
462	C₂²⋊C₄	—	4	16	no	—
463	C₂²⋊C₄	—	4	8	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	8	no	—
473	C₂³	—	2	8	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	4	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	4	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	4	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	4	no	—
501	C₂³	—	4	4	no	—
502	C₂³	—	4	4	no	—
503	C₂³	C₁₉×#124	1	4	yes	—
504	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
505	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
506	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
507	C₂³	C₂×#41×C₁₉	1	2	yes	—
508	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
509	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
511	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
512	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
513	Q₈	—	4	16	no	—
514	D₄	—	4	16	no	—
515	D₄	—	4	32	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	8	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	4	16	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	C₁₉×#120	1	4	yes	—
548	C₂×C₄	C₁₉×#120	1	4	yes	—
549	C₂²	—	2	4	no	—
550	C₂²	—	2	4	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	8	no	—
554	C₂²	—	4	8	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	8	no	—
560	C₂²	—	4	8	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	8	4	no	—
564	C₂²	—	8	4	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	2	no	—
567	C₂²	—	8	2	no	—
568	C₂²	—	8	2	no	—
569	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
570	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
571	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
572	C₂²	C₁₉×#534	1	1	yes	characteristic
573	C₂²	C₁₉×#535	1	2	yes	—
574	C₂²	C₁₉×#535	1	1	yes	characteristic
575	C₂²	C₁₉×#536	1	2	yes	—
576	C₂²	C₁₉×#536	1	1	yes	characteristic
577	C₂²	C₁₉×#537	1	2	yes	—
578	C₂²	C₁₉×#537	1	2	yes	—
579	C₂²	C₁₉×#537	1	1	yes	characteristic
580	C₂²	C₁₉×#538	1	2	yes	—
581	C₂²	C₁₉×#539	1	2	yes	—
582	C₂²	D₄²×C₁₉	1	4	yes	—
583	C₂²	C₁₉×#546	1	4	yes	—
584	C₂²	C₁₉×#548	1	4	yes	—
585	C₂²	C₁₉×#562	1	4	yes	—
586	C₄	—	2	4	no	—
587	C₄	—	2	4	no	—
588	C₄	—	4	4	no	—
589	C₄	—	4	4	no	—
590	C₄	—	4	4	no	—
591	C₄	—	8	4	no	—
592	C₂	—	4	4	no	—
593	C₂	—	8	4	no	—
594	C₂	C₁₉×#2403	1	1	yes	characteristic
595	C₂	C₁₉×#2435	1	1	yes	characteristic
596	C₂	C₁₉×#2436	1	1	yes	characteristic
597	C₂	C₁₉×#2615	1	1	yes	characteristic
598	C₂	C₁₉×#2616	1	1	yes	characteristic
599	C₂	C₁₉×#2639	1	1	yes	characteristic
600	C₂	C₁₉×#2676	1	4	yes	—
601	C₂	C₁₉×#2681	1	4	yes	—
602	C₂	C₁₉×#2816	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×#121	C₂
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×C₂²⋊Q₈	C₂	semidirect
3. C₂×C₁₉×#394	C₂	semidirect
4. C₂×C₁₉×#393	C₂	semidirect
5. C₁₉×#1441	C₂	semidirect
6. C₁₉×#1439	C₂	semidirect
7. C₁₉×#1438	C₂	semidirect
8. C₁₉×C₂²⋊#95	C₂	semidirect
64. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
162. #16253	C₁₉	direct (N × H)
248. C₂²×C₂²⋊Q₈	C₂×C₁₉	semidirect
250. C₂×#394	C₂×C₁₉	semidirect
251. C₂×#393	C₂×C₁₉	semidirect
252. #1441	C₂×C₁₉	semidirect
253. #1439	C₂×C₁₉	semidirect
254. #1438	C₂×C₁₉	semidirect
255. C₂²⋊#95	C₂×C₁₉	semidirect
365. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
385. C₁₉	#16253	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊Q₈	2
C₂²×C₁₉×#121	2
C₂×C₁₉×#394	2
C₂×C₁₉×#393	2
C₁₉×#1441	2
C₁₉×#1439	2
C₁₉×#1438	2
C₁₉×C₂²⋊#95	2
#16253	19

Subgroups — C19×#16253 #18022212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#16253 #18022212