Subgroups — C₁₉×#24015 #18029974

Order 4864.

1468 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#482	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2034	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1854	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1786	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1780	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#535	—	2	8	no	—
13	C₂×C₁₉×#127	—	2	1	no	—
14	C₂×C₁₉×#124	—	2	1	no	—
15	C₂×C₁₉×#121	C₂²	1	2	yes	—
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₂×C₁₉×#120	—	2	1	no	—
18	C₂×C₁₉×#120	—	2	1	no	—
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#482	—	2	8	no	—
23	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
24	C₂×C₁₉×#106	C₂²	1	2	yes	complemented
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×#102	C₂²	1	2	yes	—
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
30	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	complemented
31	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#391	—	2	1	no	—
34	C₁₉×#390	—	2	1	no	—
35	C₁₉×#386	—	2	1	no	—
36	C₁₉×#386	—	2	1	no	—
37	C₁₉×#380	C₂²	1	2	yes	—
38	C₁₉×#380	C₂²	1	2	yes	complemented
39	C₁₉×#340	C₂²	1	2	yes	complemented
40	C₁₉×#340	C₂²	1	2	yes	complemented
41	C₂⁵×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	2	4	no	—
43	C₂×#41×C₁₉	—	2	4	no	—
44	C₂×#41×C₁₉	—	4	1	no	—
45	C₂×#41×C₁₉	—	4	1	no	—
46	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₉	—	2	2	no	—
48	C₂²×D₄×C₁₉	—	2	2	no	—
49	C₂²×D₄×C₁₉	—	2	4	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂²×D₄×C₁₉	—	2	4	no	—
52	C₂²×D₄×C₁₉	—	4	1	no	—
53	C₂²×D₄×C₁₉	—	4	1	no	—
54	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	—	2	1	no	—
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
64	C₁₉×#127	—	2	8	no	—
65	C₁₉×#124	—	2	8	no	—
66	C₁₉×#121	—	2	4	no	—
67	C₁₉×#121	—	2	4	no	—
68	C₁₉×#121	—	2	4	no	—
69	C₁₉×#121	D₄	1	8	yes	—
70	C₁₉×#120	—	2	8	no	—
71	C₁₉×#120	—	2	8	no	—
72	C₁₉×#117	—	2	4	no	—
73	C₁₉×#117	—	2	4	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
76	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₄²×C₁₉	—	2	1	no	—
87	C₂×C₄²×C₁₉	—	2	1	no	—
88	C₁₉×#107	—	2	4	no	—
89	C₁₉×#106	—	2	4	no	—
90	C₁₉×#102	—	2	4	no	—
91	C₁₉×#102	—	2	4	no	—
92	C₁₉×#102	—	4	2	no	—
93	C₁₉×#102	—	4	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	4	no	—
95	C₁₉×C₂²⋊C₈	—	2	4	no	—
96	C₁₉×C₂²⋊C₈	—	4	1	no	—
97	C₁₉×C₂²⋊C₈	—	4	1	no	—
98	C₁₉×#95	—	2	2	no	—
99	C₁₉×#95	—	2	2	no	—
100	C₂⁴×C₁₉	—	2	4	no	—
101	C₂⁴×C₁₉	—	2	2	no	—
102	C₂⁴×C₁₉	—	4	2	no	—
103	C₂⁴×C₁₉	—	4	2	no	—
104	C₂⁴×C₁₉	—	8	2	no	—
105	C₂⁴×C₁₉	—	8	2	no	—
106	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
109	#41×C₁₉	—	4	8	no	—
110	#41×C₁₉	—	4	8	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	4	1	no	—
114	C₂×D₄×C₁₉	—	2	4	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	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	8	no	—
120	C₂×D₄×C₁₉	—	2	8	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	—	2	2	no	—
124	C₂×D₄×C₁₉	—	2	2	no	—
125	C₂×D₄×C₁₉	—	2	2	no	—
126	C₂×D₄×C₁₉	—	2	2	no	—
127	C₂×D₄×C₁₉	—	2	2	no	—
128	C₂×D₄×C₁₉	—	4	8	no	—
129	C₂×D₄×C₁₉	—	4	8	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	—	4	1	no	—
132	C₂×D₄×C₁₉	—	4	1	no	—
133	C₂×D₄×C₁₉	—	4	2	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	8	2	no	—
136	C₂×D₄×C₁₉	—	8	2	no	—
137	C₂×D₄×C₁₉	—	8	2	no	—
138	C₂×D₄×C₁₉	—	8	2	no	—
139	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	1	no	—
144	C₂²×C₄×C₁₉	—	2	1	no	—
145	C₂²×C₄×C₁₉	—	2	1	no	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	2	no	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	4	2	no	—
154	C₂²×C₄×C₁₉	—	8	2	no	—
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	#41	1	4	yes	—
160	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	2	no	—
163	C₂×C₈×C₁₉	—	2	2	no	—
164	C₂×C₈×C₁₉	—	2	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	4	2	no	—
173	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
174	C₂²⋊C₄×C₁₉	—	2	4	no	—
175	C₂²⋊C₄×C₁₉	—	2	8	no	—
176	C₂²⋊C₄×C₁₉	—	2	8	no	—
177	C₂²⋊C₄×C₁₉	—	4	2	no	—
178	C₂²⋊C₄×C₁₉	—	8	2	no	—
179	C₂²⋊C₄×C₁₉	—	8	2	no	—
180	C₄²×C₁₉	—	2	4	no	—
181	C₄²×C₁₉	—	4	2	no	—
182	#24015	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₉	—	2	1	no	—
184	C₂³×C₁₉	—	2	1	no	—
185	C₂³×C₁₉	—	2	1	no	—
186	C₂³×C₁₉	—	2	1	no	—
187	C₂³×C₁₉	—	2	2	no	—
188	C₂³×C₁₉	—	2	2	no	—
189	C₂³×C₁₉	—	2	2	no	—
190	C₂³×C₁₉	—	2	2	no	—
191	C₂³×C₁₉	—	2	4	no	—
192	C₂³×C₁₉	—	2	1	no	—
193	C₂³×C₁₉	—	2	1	no	—
194	C₂³×C₁₉	—	2	1	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	4	8	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	4	2	no	—
200	C₂³×C₁₉	—	4	2	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	8	8	no	—
205	C₂³×C₁₉	—	8	8	no	—
206	C₂³×C₁₉	—	8	4	no	—
207	C₂³×C₁₉	—	8	4	no	—
208	C₂³×C₁₉	#120	1	2	yes	—
209	C₂³×C₁₉	#123	1	2	yes	—
210	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₉	—	4	4	no	—
212	D₄×C₁₉	—	2	4	no	—
213	D₄×C₁₉	—	2	4	no	—
214	D₄×C₁₉	—	4	4	no	—
215	D₄×C₁₉	—	4	4	no	—
216	D₄×C₁₉	—	4	8	no	—
217	D₄×C₁₉	—	4	4	no	—
218	D₄×C₁₉	—	4	2	no	—
219	D₄×C₁₉	—	4	2	no	—
220	D₄×C₁₉	—	8	8	no	—
221	D₄×C₁₉	—	8	8	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	4	no	—
227	C₂×C₄×C₁₉	—	2	4	no	—
228	C₂×C₄×C₁₉	—	2	4	no	—
229	C₂×C₄×C₁₉	—	2	4	no	—
230	C₂×C₄×C₁₉	—	2	4	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	2	1	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	2	no	—
238	C₂×C₄×C₁₉	—	4	2	no	—
239	C₂×C₄×C₁₉	—	4	2	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	2	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	8	4	no	—
245	C₂×C₄×C₁₉	#120	1	2	yes	—
246	C₂×C₄×C₁₉	#123	1	2	yes	—
247	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
249	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
251	C₈×C₁₉	—	4	2	no	—
252	C₈×C₁₉	—	4	2	no	—
253	C₂×#535	C₂×C₁₉	1	1	yes	characteristic
254	C₂×#482	C₂×C₁₉	1	2	yes	complemented
255	#2311	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#2034	C₂×C₁₉	1	2	yes	complemented
257	#2033	C₂×C₁₉	1	2	yes	complemented
258	#1874	C₂×C₁₉	1	2	yes	complemented
259	#1854	C₂×C₁₉	1	2	yes	complemented
260	#1786	C₂×C₁₉	1	2	yes	complemented
261	#1780	C₂×C₁₉	1	1	yes	characteristic, complemented
262	C₂²×C₁₉	—	2	4	no	—
263	C₂²×C₁₉	—	2	2	no	—
264	C₂²×C₁₉	—	2	2	no	—
265	C₂²×C₁₉	—	2	4	no	—
266	C₂²×C₁₉	—	4	2	no	—
267	C₂²×C₁₉	—	4	1	no	—
268	C₂²×C₁₉	—	4	1	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	1	no	—
271	C₂²×C₁₉	—	4	2	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	1	no	—
274	C₂²×C₁₉	—	4	4	no	—
275	C₂²×C₁₉	—	4	1	no	—
276	C₂²×C₁₉	—	4	1	no	—
277	C₂²×C₁₉	—	4	2	no	—
278	C₂²×C₁₉	—	4	4	no	—
279	C₂²×C₁₉	—	4	4	no	—
280	C₂²×C₁₉	—	8	16	no	—
281	C₂²×C₁₉	—	8	2	no	—
282	C₂²×C₁₉	—	8	2	no	—
283	C₂²×C₁₉	—	8	2	no	—
284	C₂²×C₁₉	—	8	2	no	—
285	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
286	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
287	C₂²×C₁₉	#534	1	1	yes	characteristic
288	C₂²×C₁₉	#576	1	2	yes	—
289	C₂²×C₁₉	#577	1	2	yes	—
290	C₄×C₁₉	—	2	2	no	—
291	C₄×C₁₉	—	2	2	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	4	no	—
294	C₄×C₁₉	—	8	2	no	—
295	C₄×C₁₉	—	8	2	no	—
296	C₄×C₁₉	#546	1	2	yes	—
297	C₄×C₁₉	#546	1	2	yes	—
298	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
299	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
300	#535	—	2	8	no	—
301	C₂×#127	—	2	1	no	—
302	C₂×#124	—	2	1	no	—
303	C₂×#121	C₂²×C₁₉	1	2	yes	—
304	C₂×#121	C₂²×C₁₉	1	2	yes	—
305	C₂×#120	—	2	1	no	—
306	C₂×#120	—	2	1	no	—
307	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
309	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
310	#482	—	2	8	no	—
311	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
312	C₂×#106	C₂²×C₁₉	1	2	yes	complemented
313	C₂×#102	C₂²×C₁₉	1	2	yes	—
314	C₂×#102	C₂²×C₁₉	1	2	yes	—
315	C₂×#102	C₂²×C₁₉	1	2	yes	—
316	C₂×#102	C₂²×C₁₉	1	2	yes	—
317	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
318	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	complemented
319	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
320	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
321	#391	—	2	1	no	—
322	#390	—	2	1	no	—
323	#386	—	2	1	no	—
324	#386	—	2	1	no	—
325	#380	C₂²×C₁₉	1	2	yes	—
326	#380	C₂²×C₁₉	1	2	yes	complemented
327	#340	C₂²×C₁₉	1	2	yes	complemented
328	#340	C₂²×C₁₉	1	2	yes	complemented
329	C₂×C₁₉	—	4	2	no	—
330	C₂×C₁₉	—	4	2	no	—
331	C₂×C₁₉	—	8	1	no	—
332	C₂×C₁₉	—	8	4	no	—
333	C₂×C₁₉	#2405	1	1	yes	characteristic
334	C₂×C₁₉	#3012	1	2	yes	—
335	C₂×C₁₉	#3096	1	2	yes	—
336	C₂×C₁₉	#3199	1	1	yes	characteristic
337	C₂×C₁₉	#3200	1	1	yes	characteristic
338	C₂⁵	—	2	1	no	—
339	C₂×#41	—	2	4	no	—
340	C₂×#41	—	2	4	no	—
341	C₂×#41	—	4	1	no	—
342	C₂×#41	—	4	1	no	—
343	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	—	2	2	no	—
346	C₂²×D₄	—	2	4	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	—	2	4	no	—
349	C₂²×D₄	—	4	1	no	—
350	C₂²×D₄	—	4	1	no	—
351	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
352	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
353	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
354	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
357	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
360	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
361	#127	—	2	8	no	—
362	#124	—	2	8	no	—
363	#121	—	2	4	no	—
364	#121	—	2	4	no	—
365	#121	—	2	4	no	—
366	#121	D₄×C₁₉	1	8	yes	—
367	#120	—	2	8	no	—
368	#120	—	2	8	no	—
369	#117	—	2	4	no	—
370	#117	—	2	4	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	—	4	1	no	—
373	C₂×C₄⋊C₄	—	4	1	no	—
374	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	#107	—	2	4	no	—
386	#106	—	2	4	no	—
387	#102	—	2	4	no	—
388	#102	—	2	4	no	—
389	#102	—	4	2	no	—
390	#102	—	4	2	no	—
391	C₂²⋊C₈	—	2	4	no	—
392	C₂²⋊C₈	—	2	4	no	—
393	C₂²⋊C₈	—	4	1	no	—
394	C₂²⋊C₈	—	4	1	no	—
395	#95	—	2	2	no	—
396	#95	—	2	2	no	—
397	C₁₉	#24015	1	1	yes	characteristic, direct product factor, Sylow
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	—	4	2	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	8	2	no	—
403	C₂⁴	—	8	2	no	—
404	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
407	#41	—	4	8	no	—
408	#41	—	4	8	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	4	1	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	4	8	no	—
427	C₂×D₄	—	4	8	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	2	no	—
432	C₂×D₄	—	4	2	no	—
433	C₂×D₄	—	8	2	no	—
434	C₂×D₄	—	8	2	no	—
435	C₂×D₄	—	8	2	no	—
436	C₂×D₄	—	8	2	no	—
437	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	8	2	no	—
453	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	#41×C₁₉	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	4	2	no	—
471	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	8	2	no	—
477	C₂²⋊C₄	—	8	2	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	4	2	no	—
480	C₂³	—	2	1	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	1	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	4	8	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	8	8	no	—
502	C₂³	—	8	8	no	—
503	C₂³	—	8	4	no	—
504	C₂³	—	8	4	no	—
505	C₂³	C₁₉×#120	1	2	yes	—
506	C₂³	C₁₉×#123	1	2	yes	—
507	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
508	Q₈	—	4	4	no	—
509	D₄	—	2	4	no	—
510	D₄	—	2	4	no	—
511	D₄	—	4	4	no	—
512	D₄	—	4	4	no	—
513	D₄	—	4	8	no	—
514	D₄	—	4	4	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	8	8	no	—
518	D₄	—	8	8	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	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	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	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	8	4	no	—
542	C₂×C₄	C₁₉×#120	1	2	yes	—
543	C₂×C₄	C₁₉×#123	1	2	yes	—
544	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
545	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
546	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
548	C₈	—	4	2	no	—
549	C₈	—	4	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	8	16	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	2	no	—
572	C₂²	—	8	2	no	—
573	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
574	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
575	C₂²	C₁₉×#534	1	1	yes	characteristic
576	C₂²	C₁₉×#576	1	2	yes	—
577	C₂²	C₁₉×#577	1	2	yes	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	4	no	—
582	C₄	—	8	2	no	—
583	C₄	—	8	2	no	—
584	C₄	C₁₉×#546	1	2	yes	—
585	C₄	C₁₉×#546	1	2	yes	—
586	C₂	—	4	2	no	—
587	C₂	—	4	2	no	—
588	C₂	—	8	1	no	—
589	C₂	—	8	4	no	—
590	C₂	C₁₉×#2405	1	1	yes	characteristic
591	C₂	C₁₉×#3012	1	2	yes	—
592	C₂	C₁₉×#3096	1	2	yes	—
593	C₂	C₁₉×#3199	1	1	yes	characteristic
594	C₂	C₁₉×#3200	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#535	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#482	C₂	semidirect
3. C₁₉×#2311	C₂	semidirect
4. C₁₉×#2034	C₂	semidirect
5. C₁₉×#2033	C₂	semidirect
6. C₁₉×#1874	C₂	semidirect
7. C₁₉×#1854	C₂	semidirect
8. C₁₉×#1786	C₂	semidirect
9. C₁₉×#1780	C₂	semidirect
20. C₂×C₁₉×#117	C₂²	semidirect
21. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
23. C₂×C₁₉×#107	C₂²	semidirect
24. C₂×C₁₉×#106	C₂²	semidirect
30. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
31. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
32. C₂×C₁₉×C₂²⋊C₈	C₂²	semidirect
38. C₁₉×#380	C₂²	semidirect
39. C₁₉×#340	C₂²	semidirect
40. C₁₉×#340	C₂²	semidirect
182. #24015	C₁₉	direct (N × H)
254. C₂×#482	C₂×C₁₉	semidirect
255. #2311	C₂×C₁₉	semidirect
256. #2034	C₂×C₁₉	semidirect
257. #2033	C₂×C₁₉	semidirect
258. #1874	C₂×C₁₉	semidirect
259. #1854	C₂×C₁₉	semidirect
260. #1786	C₂×C₁₉	semidirect
261. #1780	C₂×C₁₉	semidirect
308. C₂×#117	C₂²×C₁₉	semidirect
309. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
311. C₂×#107	C₂²×C₁₉	semidirect
312. C₂×#106	C₂²×C₁₉	semidirect
318. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
319. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
320. C₂×C₂²⋊C₈	C₂²×C₁₉	semidirect
326. #380	C₂²×C₁₉	semidirect
327. #340	C₂²×C₁₉	semidirect
328. #340	C₂²×C₁₉	semidirect
397. C₁₉	#24015	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×#535	2
C₂×C₁₉×#482	2
C₁₉×#2311	2
C₁₉×#2034	2
C₁₉×#2033	2
C₁₉×#1874	2
C₁₉×#1854	2
C₁₉×#1786	2
C₁₉×#1780	2
#24015	19

Subgroups — C19×#24015 #18029974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24015 #18029974