Subgroups — C₁₉×#24011 #18029970

Order 4864.

1340 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#537	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#480	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2036	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2033	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1875	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1852	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1788	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1780	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#537	—	2	4	no	—
15	C₁₉×#537	—	2	4	no	—
16	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#121	—	2	1	no	—
20	C₂×C₁₉×#121	—	2	1	no	—
21	C₂×C₁₉×#121	—	2	1	no	—
22	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₁₉×#484	—	2	4	no	—
28	C₁₉×#480	—	2	4	no	—
29	C₂×C₁₉×#107	C₂²	1	2	yes	—
30	C₂×C₁₉×#107	C₂²	1	2	yes	—
31	C₂×C₁₉×#103	C₂²	1	2	yes	—
32	C₂×C₁₉×#103	C₂²	1	2	yes	—
33	C₂×C₁₉×#102	C₂²	1	2	yes	—
34	C₂×C₁₉×#102	C₂²	1	2	yes	—
35	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₁₉×#391	—	2	1	no	—
40	C₁₉×#390	—	2	1	no	—
41	C₁₉×#386	—	2	1	no	—
42	C₁₉×#386	—	2	1	no	—
43	C₁₉×#380	C₂²	1	2	yes	—
44	C₁₉×#380	C₂²	1	2	yes	—
45	C₁₉×#340	C₂²	1	2	yes	—
46	C₁₉×#340	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	—	2	2	no	—
50	C₂×#41×C₁₉	—	2	2	no	—
51	C₂×#41×C₁₉	—	2	4	no	—
52	C₂×#41×C₁₉	—	2	4	no	—
53	C₂×#41×C₁₉	—	4	2	no	—
54	C₂×#41×C₁₉	—	4	2	no	—
55	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	—	2	1	no	—
59	C₂²×D₄×C₁₉	—	2	1	no	—
60	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
63	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₉	—	2	1	no	—
65	C₂³×C₄×C₁₉	—	2	1	no	—
66	C₂³×C₄×C₁₉	—	2	1	no	—
67	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
72	C₁₉×C₂²⋊Q₈	—	2	8	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×C₂²⋊Q₈	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	2	2	no	—
76	C₁₉×C₂²⋊Q₈	D₄	1	4	yes	—
77	C₁₉×#121	—	2	8	no	—
78	C₁₉×#121	—	2	8	no	—
79	C₁₉×#121	—	2	8	no	—
80	C₁₉×#121	—	2	2	no	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	D₄	1	4	yes	—
84	C₁₉×#117	—	4	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
90	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
91	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₄²×C₁₉	—	2	1	no	—
105	C₁₉×#107	—	2	4	no	—
106	C₁₉×#107	—	2	4	no	—
107	C₁₉×#103	—	2	4	no	—
108	C₁₉×#103	—	4	2	no	—
109	C₁₉×#102	—	2	4	no	—
110	C₁₉×#102	—	4	2	no	—
111	C₁₉×C₂²⋊C₈	—	2	2	no	—
112	C₁₉×C₂²⋊C₈	—	2	2	no	—
113	C₁₉×C₂²⋊C₈	—	2	4	no	—
114	C₁₉×C₂²⋊C₈	—	4	2	no	—
115	C₁₉×#95	—	2	2	no	—
116	C₁₉×#95	—	2	2	no	—
117	C₂⁴×C₁₉	—	2	1	no	—
118	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
121	#41×C₁₉	—	4	8	no	—
122	#41×C₁₉	—	4	8	no	—
123	#41×C₁₉	—	4	8	no	—
124	#41×C₁₉	—	4	8	no	—
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	2	1	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	—	4	1	no	—
131	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	2	no	—
135	C₂×D₄×C₁₉	—	2	2	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	4	no	—
138	C₂×D₄×C₁₉	—	2	4	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	1	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	4	1	no	—
145	C₂×D₄×C₁₉	—	4	1	no	—
146	C₂×D₄×C₁₉	—	4	1	no	—
147	C₂×D₄×C₁₉	—	4	2	no	—
148	C₂×D₄×C₁₉	—	4	2	no	—
149	C₂×D₄×C₁₉	—	8	2	no	—
150	C₂×D₄×C₁₉	—	8	2	no	—
151	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	—	2	1	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	4	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	4	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	2	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	4	2	no	—
169	C₂²×C₄×C₁₉	—	4	2	no	—
170	C₂²×C₄×C₁₉	—	4	2	no	—
171	C₂²×C₄×C₁₉	—	8	2	no	—
172	C₂²×C₄×C₁₉	—	8	2	no	—
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	2	yes	—
176	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	#41	1	4	yes	—
179	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
180	C₂×C₈×C₁₉	—	2	2	no	—
181	C₂×C₈×C₁₉	—	2	2	no	—
182	C₂×C₈×C₁₉	—	2	2	no	—
183	C₂×C₈×C₁₉	—	2	2	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₂×C₈×C₁₉	—	2	2	no	—
186	C₄⋊C₄×C₁₉	—	2	4	no	—
187	C₄⋊C₄×C₁₉	—	2	4	no	—
188	C₄⋊C₄×C₁₉	—	2	4	no	—
189	C₄⋊C₄×C₁₉	—	2	1	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	2	no	—
193	C₄⋊C₄×C₁₉	—	2	2	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	4	2	no	—
196	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
197	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²⋊C₄×C₁₉	—	2	4	no	—
199	C₂²⋊C₄×C₁₉	—	2	4	no	—
200	C₂²⋊C₄×C₁₉	—	2	4	no	—
201	C₂²⋊C₄×C₁₉	—	2	4	no	—
202	C₂²⋊C₄×C₁₉	—	4	2	no	—
203	C₂²⋊C₄×C₁₉	—	8	2	no	—
204	C₂²⋊C₄×C₁₉	—	8	2	no	—
205	C₄²×C₁₉	—	4	2	no	—
206	#24011	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₁₉	—	2	1	no	—
208	C₂³×C₁₉	—	2	1	no	—
209	C₂³×C₁₉	—	2	1	no	—
210	C₂³×C₁₉	—	2	1	no	—
211	C₂³×C₁₉	—	2	2	no	—
212	C₂³×C₁₉	—	2	2	no	—
213	C₂³×C₁₉	—	2	2	no	—
214	C₂³×C₁₉	—	2	2	no	—
215	C₂³×C₁₉	—	2	1	no	—
216	C₂³×C₁₉	—	2	2	no	—
217	C₂³×C₁₉	—	2	1	no	—
218	C₂³×C₁₉	—	2	1	no	—
219	C₂³×C₁₉	—	2	2	no	—
220	C₂³×C₁₉	—	2	2	no	—
221	C₂³×C₁₉	—	4	1	no	—
222	C₂³×C₁₉	—	4	1	no	—
223	C₂³×C₁₉	—	4	2	no	—
224	C₂³×C₁₉	—	4	2	no	—
225	C₂³×C₁₉	#120	1	2	yes	—
226	C₂³×C₁₉	#123	1	2	yes	—
227	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
228	Q₈×C₁₉	—	2	4	no	—
229	Q₈×C₁₉	—	4	4	no	—
230	Q₈×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	2	4	no	—
232	D₄×C₁₉	—	4	4	no	—
233	D₄×C₁₉	—	4	4	no	—
234	D₄×C₁₉	—	4	4	no	—
235	D₄×C₁₉	—	4	8	no	—
236	D₄×C₁₉	—	4	2	no	—
237	D₄×C₁₉	—	8	4	no	—
238	D₄×C₁₉	—	8	4	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	2	1	no	—
242	C₂×C₄×C₁₉	—	2	1	no	—
243	C₂×C₄×C₁₉	—	2	4	no	—
244	C₂×C₄×C₁₉	—	2	4	no	—
245	C₂×C₄×C₁₉	—	2	4	no	—
246	C₂×C₄×C₁₉	—	2	4	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	1	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	1	no	—
253	C₂×C₄×C₁₉	—	4	8	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	2	no	—
260	C₂×C₄×C₁₉	—	4	2	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	2	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	2	no	—
265	C₂×C₄×C₁₉	—	4	2	no	—
266	C₂×C₄×C₁₉	—	8	4	no	—
267	C₂×C₄×C₁₉	—	8	4	no	—
268	C₂×C₄×C₁₉	#120	1	2	yes	—
269	C₂×C₄×C₁₉	#123	1	2	yes	—
270	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
273	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
274	C₈×C₁₉	—	4	2	no	—
275	C₈×C₁₉	—	4	2	no	—
276	C₂×#537	C₂×C₁₉	1	1	yes	characteristic
277	C₂×#484	C₂×C₁₉	1	1	yes	characteristic, complemented
278	C₂×#480	C₂×C₁₉	1	1	yes	characteristic, complemented
279	#2311	C₂×C₁₉	1	1	yes	characteristic, complemented
280	#2036	C₂×C₁₉	1	2	yes	complemented
281	#2033	C₂×C₁₉	1	2	yes	complemented
282	#1875	C₂×C₁₉	1	1	yes	characteristic, complemented
283	#1873	C₂×C₁₉	1	1	yes	characteristic, complemented
284	#1852	C₂×C₁₉	1	2	yes	complemented
285	#1788	C₂×C₁₉	1	2	yes	complemented
286	#1780	C₂×C₁₉	1	1	yes	characteristic, complemented
287	C₂²×C₁₉	—	2	4	no	—
288	C₂²×C₁₉	—	2	2	no	—
289	C₂²×C₁₉	—	2	2	no	—
290	C₂²×C₁₉	—	2	2	no	—
291	C₂²×C₁₉	—	2	2	no	—
292	C₂²×C₁₉	—	4	2	no	—
293	C₂²×C₁₉	—	4	2	no	—
294	C₂²×C₁₉	—	4	2	no	—
295	C₂²×C₁₉	—	4	1	no	—
296	C₂²×C₁₉	—	4	1	no	—
297	C₂²×C₁₉	—	4	2	no	—
298	C₂²×C₁₉	—	4	2	no	—
299	C₂²×C₁₉	—	4	1	no	—
300	C₂²×C₁₉	—	4	2	no	—
301	C₂²×C₁₉	—	4	1	no	—
302	C₂²×C₁₉	—	4	2	no	—
303	C₂²×C₁₉	—	4	1	no	—
304	C₂²×C₁₉	—	4	2	no	—
305	C₂²×C₁₉	—	8	2	no	—
306	C₂²×C₁₉	—	8	2	no	—
307	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
308	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
309	C₂²×C₁₉	#534	1	1	yes	characteristic
310	C₂²×C₁₉	#576	1	2	yes	—
311	C₂²×C₁₉	#578	1	2	yes	—
312	C₄×C₁₉	—	2	2	no	—
313	C₄×C₁₉	—	2	2	no	—
314	C₄×C₁₉	—	4	1	no	—
315	C₄×C₁₉	—	4	2	no	—
316	C₄×C₁₉	—	4	2	no	—
317	C₄×C₁₉	—	4	2	no	—
318	C₄×C₁₉	—	8	2	no	—
319	C₄×C₁₉	—	8	2	no	—
320	C₄×C₁₉	#546	1	2	yes	—
321	C₄×C₁₉	#546	1	2	yes	—
322	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
323	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
324	#537	—	2	4	no	—
325	#537	—	2	4	no	—
326	C₂×C₂²⋊Q₈	—	2	1	no	—
327	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
328	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
329	C₂×#121	—	2	1	no	—
330	C₂×#121	—	2	1	no	—
331	C₂×#121	—	2	1	no	—
332	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
333	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
334	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
335	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
336	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
337	#484	—	2	4	no	—
338	#480	—	2	4	no	—
339	C₂×#107	C₂²×C₁₉	1	2	yes	—
340	C₂×#107	C₂²×C₁₉	1	2	yes	—
341	C₂×#103	C₂²×C₁₉	1	2	yes	—
342	C₂×#103	C₂²×C₁₉	1	2	yes	—
343	C₂×#102	C₂²×C₁₉	1	2	yes	—
344	C₂×#102	C₂²×C₁₉	1	2	yes	—
345	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
346	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
347	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
348	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
349	#391	—	2	1	no	—
350	#390	—	2	1	no	—
351	#386	—	2	1	no	—
352	#386	—	2	1	no	—
353	#380	C₂²×C₁₉	1	2	yes	—
354	#380	C₂²×C₁₉	1	2	yes	—
355	#340	C₂²×C₁₉	1	2	yes	—
356	#340	C₂²×C₁₉	1	2	yes	—
357	C₂×C₁₉	—	4	2	no	—
358	C₂×C₁₉	—	4	2	no	—
359	C₂×C₁₉	—	8	1	no	—
360	C₂×C₁₉	—	8	2	no	—
361	C₂×C₁₉	#2405	1	1	yes	characteristic
362	C₂×C₁₉	#3008	1	1	yes	characteristic
363	C₂×C₁₉	#3011	1	1	yes	characteristic
364	C₂×C₁₉	#3098	1	2	yes	—
365	C₂×C₁₉	#3203	1	2	yes	—
366	C₂×#41	—	2	2	no	—
367	C₂×#41	—	2	2	no	—
368	C₂×#41	—	2	2	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	4	no	—
371	C₂×#41	—	2	4	no	—
372	C₂×#41	—	4	2	no	—
373	C₂×#41	—	4	2	no	—
374	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
375	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
376	C₂²×D₄	—	2	1	no	—
377	C₂²×D₄	—	2	1	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
380	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
381	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
382	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
390	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
391	C₂²⋊Q₈	—	2	8	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	D₄×C₁₉	1	4	yes	—
396	#121	—	2	8	no	—
397	#121	—	2	8	no	—
398	#121	—	2	8	no	—
399	#121	—	2	2	no	—
400	#121	—	2	2	no	—
401	#121	—	2	2	no	—
402	#121	D₄×C₁₉	1	4	yes	—
403	#117	—	4	2	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	2	no	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	—	2	2	no	—
410	C₂×C₄⋊C₄	—	2	2	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	2	no	—
422	C₂×C₂²⋊C₄	—	2	2	no	—
423	C₂×C₄²	—	2	1	no	—
424	#107	—	2	4	no	—
425	#107	—	2	4	no	—
426	#103	—	2	4	no	—
427	#103	—	4	2	no	—
428	#102	—	2	4	no	—
429	#102	—	4	2	no	—
430	C₂²⋊C₈	—	2	2	no	—
431	C₂²⋊C₈	—	2	2	no	—
432	C₂²⋊C₈	—	2	4	no	—
433	C₂²⋊C₈	—	4	2	no	—
434	#95	—	2	2	no	—
435	#95	—	2	2	no	—
436	C₁₉	#24011	1	1	yes	characteristic, direct product factor, Sylow
437	C₂⁴	—	2	1	no	—
438	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
441	#41	—	4	8	no	—
442	#41	—	4	8	no	—
443	#41	—	4	8	no	—
444	#41	—	4	8	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	4	1	no	—
451	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	4	1	no	—
465	C₂×D₄	—	4	1	no	—
466	C₂×D₄	—	4	1	no	—
467	C₂×D₄	—	4	2	no	—
468	C₂×D₄	—	4	2	no	—
469	C₂×D₄	—	8	2	no	—
470	C₂×D₄	—	8	2	no	—
471	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	8	2	no	—
492	C₂²×C₄	—	8	2	no	—
493	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
495	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
496	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
497	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₂²×C₄	#41×C₁₉	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	2	2	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
517	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₂²⋊C₄	—	8	2	no	—
524	C₂²⋊C₄	—	8	2	no	—
525	C₄²	—	4	2	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	4	2	no	—
544	C₂³	C₁₉×#120	1	2	yes	—
545	C₂³	C₁₉×#123	1	2	yes	—
546	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
547	Q₈	—	2	4	no	—
548	Q₈	—	4	4	no	—
549	Q₈	—	4	2	no	—
550	D₄	—	2	4	no	—
551	D₄	—	4	4	no	—
552	D₄	—	4	4	no	—
553	D₄	—	4	4	no	—
554	D₄	—	4	8	no	—
555	D₄	—	4	2	no	—
556	D₄	—	8	4	no	—
557	D₄	—	8	4	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	8	4	no	—
586	C₂×C₄	—	8	4	no	—
587	C₂×C₄	C₁₉×#120	1	2	yes	—
588	C₂×C₄	C₁₉×#123	1	2	yes	—
589	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
590	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
591	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
592	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
593	C₈	—	4	2	no	—
594	C₈	—	4	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	8	2	no	—
614	C₂²	—	8	2	no	—
615	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
616	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
617	C₂²	C₁₉×#534	1	1	yes	characteristic
618	C₂²	C₁₉×#576	1	2	yes	—
619	C₂²	C₁₉×#578	1	2	yes	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	2	no	—
624	C₄	—	4	2	no	—
625	C₄	—	4	2	no	—
626	C₄	—	8	2	no	—
627	C₄	—	8	2	no	—
628	C₄	C₁₉×#546	1	2	yes	—
629	C₄	C₁₉×#546	1	2	yes	—
630	C₂	—	4	2	no	—
631	C₂	—	4	2	no	—
632	C₂	—	8	1	no	—
633	C₂	—	8	2	no	—
634	C₂	C₁₉×#2405	1	1	yes	characteristic
635	C₂	C₁₉×#3008	1	1	yes	characteristic
636	C₂	C₁₉×#3011	1	1	yes	characteristic
637	C₂	C₁₉×#3098	1	2	yes	—
638	C₂	C₁₉×#3203	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#537	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×#484	C₂	semidirect
3. C₂×C₁₉×#480	C₂	semidirect
4. C₁₉×#2311	C₂	semidirect
5. C₁₉×#2036	C₂	semidirect
6. C₁₉×#2033	C₂	semidirect
7. C₁₉×#1875	C₂	semidirect
8. C₁₉×#1873	C₂	semidirect
9. C₁₉×#1852	C₂	semidirect
10. C₁₉×#1788	C₂	semidirect
11. C₁₉×#1780	C₂	semidirect
206. #24011	C₁₉	direct (N × H)
277. C₂×#484	C₂×C₁₉	semidirect
278. C₂×#480	C₂×C₁₉	semidirect
279. #2311	C₂×C₁₉	semidirect
280. #2036	C₂×C₁₉	semidirect
281. #2033	C₂×C₁₉	semidirect
282. #1875	C₂×C₁₉	semidirect
283. #1873	C₂×C₁₉	semidirect
284. #1852	C₂×C₁₉	semidirect
285. #1788	C₂×C₁₉	semidirect
286. #1780	C₂×C₁₉	semidirect
436. C₁₉	#24011	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×#537	2
C₂×C₁₉×#484	2
C₂×C₁₉×#480	2
C₁₉×#2311	2
C₁₉×#2036	2
C₁₉×#2033	2
C₁₉×#1875	2
C₁₉×#1873	2
C₁₉×#1852	2
C₁₉×#1788	2
C₁₉×#1780	2
#24011	19

Subgroups — C19×#24011 #18029970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24011 #18029970