Subgroups — C₁₉×#60370 #18066329

Order 4864.

4746 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#585	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₉×#137	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3011	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3009	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3007	C₂	1	8	yes	maximal, complemented
7	C₁₉×#2896	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2879	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#585	—	2	16	no	—
10	C₂×C₁₉×2₋¹⁺⁴	—	2	1	no	—
11	C₂×C₁₉×2₋¹⁺⁴	C₂²	1	4	yes	—
12	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
13	C₂×C₁₉×H(5,𝔽₂)	—	2	1	no	—
14	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	4	yes	—
15	C₂²×#41×C₁₉	—	2	4	no	—
16	C₂²×#41×C₁₉	C₂²	1	4	yes	—
17	C₂²×#41×C₁₉	C₂²	1	2	yes	—
18	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₉×#137	—	2	16	no	—
21	C₂×C₁₉×#137	C₂²	1	8	yes	complemented
22	C₂×C₁₉×#137	C₂²	1	8	yes	complemented
23	C₂²×Q₁₆×C₁₉	C₂²	1	4	yes	complemented
24	C₂²×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
25	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
26	C₁₉×#536	—	2	4	no	—
27	C₁₉×#536	C₂²	1	8	yes	complemented
28	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
29	C₂×C₁₉×#124	—	2	1	no	—
30	C₂×C₁₉×#123	—	2	2	no	—
31	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	complemented
32	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#452	C₂²	1	32	yes	complemented
34	C₁₉×#451	C₂²	1	16	yes	complemented
35	C₁₉×#450	C₂²	1	16	yes	complemented
36	C₁₉×#419	C₂²	1	4	yes	complemented
37	C₁₉×#418	C₂²	1	4	yes	complemented
38	C₁₉×#417	C₂²	1	8	yes	complemented
39	C₁₉×#416	C₂²	1	8	yes	complemented
40	C₁₉×#408	C₂²	1	8	yes	complemented
41	C₁₉×#407	C₂²	1	4	yes	complemented
42	C₁₉×2₋¹⁺⁴	—	2	16	no	—
43	C₁₉×2₋¹⁺⁴	—	2	16	no	—
44	C₁₉×2₋¹⁺⁴	—	2	16	no	—
45	C₁₉×H(5,𝔽₂)	—	2	16	no	—
46	C₁₉×H(5,𝔽₂)	—	2	32	no	—
47	C₁₉×H(5,𝔽₂)	—	2	16	no	—
48	C₁₉×H(5,𝔽₂)	—	2	16	no	—
49	C₂×#41×C₁₉	—	2	64	no	—
50	C₂×#41×C₁₉	—	2	32	no	—
51	C₂×#41×C₁₉	—	2	4	no	—
52	C₂×#41×C₁₉	—	2	8	no	—
53	C₂×#41×C₁₉	—	2	4	no	—
54	C₂×#41×C₁₉	—	2	4	no	—
55	C₂×#41×C₁₉	—	2	2	no	—
56	C₂×#41×C₁₉	—	2	4	no	—
57	C₂×#41×C₁₉	—	2	2	no	—
58	C₂×#41×C₁₉	—	2	8	no	—
59	C₂×#41×C₁₉	—	2	8	no	—
60	C₂×#41×C₁₉	D₄	1	16	yes	—
61	C₂×#41×C₁₉	D₄	1	4	yes	—
62	C₂×#41×C₁₉	C₂³	1	8	yes	—
63	C₂×#41×C₁₉	C₂³	1	4	yes	—
64	C₂×#41×C₁₉	C₂³	1	4	yes	—
65	C₂×#41×C₁₉	C₂³	1	4	yes	—
66	C₂²×Q₈×C₁₉	—	2	4	no	—
67	C₂²×Q₈×C₁₉	—	2	1	no	—
68	C₂²×Q₈×C₁₉	—	2	2	no	—
69	C₂²×Q₈×C₁₉	—	2	8	no	—
70	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
71	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
72	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
73	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
74	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₉	—	2	4	no	—
76	C₂²×D₄×C₁₉	—	2	2	no	—
77	C₂²×D₄×C₁₉	—	2	8	no	—
78	C₂²×D₄×C₁₉	—	2	4	no	—
79	C₂²×D₄×C₁₉	D₄	1	2	yes	—
80	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₉	—	2	4	no	—
84	C₂³×C₄×C₁₉	—	2	2	no	—
85	C₂³×C₄×C₁₉	—	2	1	no	—
86	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
88	C₁₉×#137	—	2	32	no	—
89	C₁₉×#137	—	2	32	no	—
90	C₂×Q₁₆×C₁₉	—	2	16	no	—
91	C₂×Q₁₆×C₁₉	C₂³	1	16	yes	—
92	C₂×SD₁₆×C₁₉	—	2	16	no	—
93	C₂×SD₁₆×C₁₉	C₂³	1	16	yes	—
94	C₂×M₁₆×C₁₉	—	2	8	no	—
95	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
96	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
97	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
98	C₁₉×C₄⋊Q₈	—	2	8	no	—
99	C₁₉×#124	—	2	8	no	—
100	C₁₉×#123	—	2	16	no	—
101	C₁₉×C₂²⋊Q₈	—	2	8	no	—
102	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
103	C₁₉×#117	—	2	2	no	—
104	C₁₉×#117	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
106	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
109	C₂×C₄²×C₁₉	—	2	1	no	—
110	C₁₉×#103	C₂³	1	16	yes	—
111	C₁₉×#102	C₂³	1	16	yes	—
112	C₁₉×C₂²⋊C₈	C₂³	1	16	yes	—
113	C₂⁴×C₁₉	—	2	4	no	—
114	C₂⁴×C₁₉	—	2	2	no	—
115	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
116	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
117	#41×C₁₉	—	2	32	no	—
118	#41×C₁₉	—	2	64	no	—
119	#41×C₁₉	—	2	32	no	—
120	#41×C₁₉	—	2	32	no	—
121	#41×C₁₉	—	2	32	no	—
122	#41×C₁₉	—	2	16	no	—
123	#41×C₁₉	—	2	16	no	—
124	#41×C₁₉	—	2	16	no	—
125	#41×C₁₉	—	2	16	no	—
126	#41×C₁₉	—	2	16	no	—
127	#41×C₁₉	—	2	8	no	—
128	#41×C₁₉	—	2	8	no	—
129	#41×C₁₉	—	2	8	no	—
130	#41×C₁₉	—	2	8	no	—
131	#41×C₁₉	C₂×D₄	1	16	yes	—
132	#41×C₁₉	C₂×D₄	1	16	yes	—
133	C₂×Q₈×C₁₉	—	2	32	no	—
134	C₂×Q₈×C₁₉	—	2	16	no	—
135	C₂×Q₈×C₁₉	—	2	4	no	—
136	C₂×Q₈×C₁₉	—	2	4	no	—
137	C₂×Q₈×C₁₉	—	2	2	no	—
138	C₂×Q₈×C₁₉	—	2	4	no	—
139	C₂×Q₈×C₁₉	—	2	2	no	—
140	C₂×Q₈×C₁₉	—	2	4	no	—
141	C₂×Q₈×C₁₉	—	2	8	no	—
142	C₂×Q₈×C₁₉	—	2	8	no	—
143	C₂×Q₈×C₁₉	—	2	8	no	—
144	C₂×Q₈×C₁₉	—	4	8	no	—
145	C₂×Q₈×C₁₉	—	4	4	no	—
146	C₂×Q₈×C₁₉	C₂×D₄	1	8	yes	—
147	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
148	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
149	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
150	C₂×D₄×C₁₉	—	2	32	no	—
151	C₂×D₄×C₁₉	—	2	64	no	—
152	C₂×D₄×C₁₉	—	2	32	no	—
153	C₂×D₄×C₁₉	—	2	16	no	—
154	C₂×D₄×C₁₉	—	2	8	no	—
155	C₂×D₄×C₁₉	—	2	8	no	—
156	C₂×D₄×C₁₉	—	2	4	no	—
157	C₂×D₄×C₁₉	—	2	4	no	—
158	C₂×D₄×C₁₉	—	2	16	no	—
159	C₂×D₄×C₁₉	—	2	4	no	—
160	C₂×D₄×C₁₉	—	2	4	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	4	no	—
163	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
164	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
165	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
166	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₉	—	2	32	no	—
168	C₂²×C₄×C₁₉	—	2	4	no	—
169	C₂²×C₄×C₁₉	—	2	2	no	—
170	C₂²×C₄×C₁₉	—	2	16	no	—
171	C₂²×C₄×C₁₉	—	2	4	no	—
172	C₂²×C₄×C₁₉	—	2	8	no	—
173	C₂²×C₄×C₁₉	—	2	4	no	—
174	C₂²×C₄×C₁₉	—	2	8	no	—
175	C₂²×C₄×C₁₉	—	2	2	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	4	no	—
178	C₂²×C₄×C₁₉	—	4	4	no	—
179	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
184	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
187	Q₁₆×C₁₉	—	2	32	no	—
188	SD₁₆×C₁₉	—	2	32	no	—
189	M₁₆×C₁₉	—	2	8	no	—
190	M₁₆×C₁₉	—	2	8	no	—
191	C₂×C₈×C₁₉	—	2	8	no	—
192	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
193	C₄⋊C₄×C₁₉	—	2	16	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
196	C₂²⋊C₄×C₁₉	—	2	4	no	—
197	C₂²⋊C₄×C₁₉	—	2	16	no	—
198	C₄²×C₁₉	—	2	4	no	—
199	#60370	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂³×C₁₉	—	2	16	no	—
201	C₂³×C₁₉	—	2	4	no	—
202	C₂³×C₁₉	—	2	4	no	—
203	C₂³×C₁₉	—	2	8	no	—
204	C₂³×C₁₉	—	4	2	no	—
205	C₂³×C₁₉	—	4	4	no	—
206	C₂³×C₁₉	—	8	4	no	—
207	C₂³×C₁₉	—	8	8	no	—
208	C₂³×C₁₉	#120	1	4	yes	—
209	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
210	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₁₉	—	2	16	no	—
213	Q₈×C₁₉	—	2	8	no	—
214	Q₈×C₁₉	—	2	8	no	—
215	Q₈×C₁₉	—	2	4	no	—
216	Q₈×C₁₉	—	2	8	no	—
217	Q₈×C₁₉	—	4	4	no	—
218	Q₈×C₁₉	—	4	8	no	—
219	Q₈×C₁₉	C₂²×D₄	1	8	yes	—
220	D₄×C₁₉	—	2	32	no	—
221	D₄×C₁₉	—	2	16	no	—
222	D₄×C₁₉	—	2	16	no	—
223	D₄×C₁₉	—	2	16	no	—
224	D₄×C₁₉	—	2	16	no	—
225	D₄×C₁₉	—	2	8	no	—
226	D₄×C₁₉	—	2	8	no	—
227	D₄×C₁₉	—	2	4	no	—
228	D₄×C₁₉	C₂²×D₄	1	8	yes	—
229	C₂×C₄×C₁₉	—	2	16	no	—
230	C₂×C₄×C₁₉	—	2	32	no	—
231	C₂×C₄×C₁₉	—	2	8	no	—
232	C₂×C₄×C₁₉	—	2	4	no	—
233	C₂×C₄×C₁₉	—	2	4	no	—
234	C₂×C₄×C₁₉	—	2	16	no	—
235	C₂×C₄×C₁₉	—	2	8	no	—
236	C₂×C₄×C₁₉	—	2	16	no	—
237	C₂×C₄×C₁₉	—	2	8	no	—
238	C₂×C₄×C₁₉	—	2	4	no	—
239	C₂×C₄×C₁₉	—	2	4	no	—
240	C₂×C₄×C₁₉	—	4	4	no	—
241	C₂×C₄×C₁₉	—	4	4	no	—
242	C₂×C₄×C₁₉	—	4	8	no	—
243	C₂×C₄×C₁₉	#120	1	8	yes	—
244	C₂×C₄×C₁₉	#120	1	4	yes	—
245	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
249	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
250	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
251	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
252	C₈×C₁₉	—	2	8	no	—
253	C₂×#585	C₂×C₁₉	1	1	yes	characteristic
254	C₂²×#137	C₂×C₁₉	1	2	yes	complemented
255	C₂×#536	C₂×C₁₉	1	1	yes	characteristic, complemented
256	#3011	C₂×C₁₉	1	8	yes	complemented
257	#3009	C₂×C₁₉	1	8	yes	complemented
258	#3007	C₂×C₁₉	1	8	yes	complemented
259	#2896	C₂×C₁₉	1	2	yes	complemented
260	#2879	C₂×C₁₉	1	1	yes	characteristic, complemented
261	C₂²×C₁₉	—	2	2	no	—
262	C₂²×C₁₉	—	2	4	no	—
263	C₂²×C₁₉	—	2	8	no	—
264	C₂²×C₁₉	—	2	4	no	—
265	C₂²×C₁₉	—	2	8	no	—
266	C₂²×C₁₉	—	4	4	no	—
267	C₂²×C₁₉	—	4	8	no	—
268	C₂²×C₁₉	—	8	4	no	—
269	C₂²×C₁₉	—	8	8	no	—
270	C₂²×C₁₉	—	8	16	no	—
271	C₂²×C₁₉	C₂×#120	1	4	yes	—
272	C₂²×C₁₉	C₂×#120	1	2	yes	—
273	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
274	C₄×C₁₉	—	2	8	no	—
275	C₄×C₁₉	—	2	4	no	—
276	C₄×C₁₉	—	4	4	no	—
277	C₄×C₁₉	—	4	4	no	—
278	C₄×C₁₉	C₂×#120	1	2	yes	—
279	C₄×C₁₉	C₂×#120	1	4	yes	—
280	C₄×C₁₉	C₂³×D₄	1	2	yes	—
281	#585	—	2	16	no	—
282	C₂×2₋¹⁺⁴	—	2	1	no	—
283	C₂×2₋¹⁺⁴	C₂²×C₁₉	1	4	yes	—
284	C₂×H(5,𝔽₂)	—	2	2	no	—
285	C₂×H(5,𝔽₂)	—	2	1	no	—
286	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	4	yes	—
287	C₂²×#41	—	2	4	no	—
288	C₂²×#41	C₂²×C₁₉	1	4	yes	—
289	C₂²×#41	C₂²×C₁₉	1	2	yes	—
290	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
291	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
292	C₂×#137	—	2	16	no	—
293	C₂×#137	C₂²×C₁₉	1	8	yes	complemented
294	C₂×#137	C₂²×C₁₉	1	8	yes	complemented
295	C₂²×Q₁₆	C₂²×C₁₉	1	4	yes	complemented
296	C₂²×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
297	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
298	#536	—	2	4	no	—
299	#536	C₂²×C₁₉	1	8	yes	complemented
300	C₂×C₄⋊Q₈	—	2	1	no	—
301	C₂×#124	—	2	1	no	—
302	C₂×#123	—	2	2	no	—
303	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	complemented
304	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
305	#452	C₂²×C₁₉	1	32	yes	complemented
306	#451	C₂²×C₁₉	1	16	yes	complemented
307	#450	C₂²×C₁₉	1	16	yes	complemented
308	#419	C₂²×C₁₉	1	4	yes	complemented
309	#418	C₂²×C₁₉	1	4	yes	complemented
310	#417	C₂²×C₁₉	1	8	yes	complemented
311	#416	C₂²×C₁₉	1	8	yes	complemented
312	#408	C₂²×C₁₉	1	8	yes	complemented
313	#407	C₂²×C₁₉	1	4	yes	complemented
314	C₂×C₁₉	—	2	2	no	—
315	C₂×C₁₉	—	2	4	no	—
316	C₂×C₁₉	—	4	4	no	—
317	C₂×C₁₉	—	4	8	no	—
318	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
319	C₂×C₁₉	#3586	1	2	yes	—
320	2₋¹⁺⁴	—	2	16	no	—
321	2₋¹⁺⁴	—	2	16	no	—
322	2₋¹⁺⁴	—	2	16	no	—
323	H(5,𝔽₂)	—	2	16	no	—
324	H(5,𝔽₂)	—	2	32	no	—
325	H(5,𝔽₂)	—	2	16	no	—
326	H(5,𝔽₂)	—	2	16	no	—
327	C₂×#41	—	2	64	no	—
328	C₂×#41	—	2	32	no	—
329	C₂×#41	—	2	4	no	—
330	C₂×#41	—	2	8	no	—
331	C₂×#41	—	2	4	no	—
332	C₂×#41	—	2	4	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	4	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	8	no	—
337	C₂×#41	—	2	8	no	—
338	C₂×#41	D₄×C₁₉	1	16	yes	—
339	C₂×#41	D₄×C₁₉	1	4	yes	—
340	C₂×#41	C₂³×C₁₉	1	8	yes	—
341	C₂×#41	C₂³×C₁₉	1	4	yes	—
342	C₂×#41	C₂³×C₁₉	1	4	yes	—
343	C₂×#41	C₂³×C₁₉	1	4	yes	—
344	C₂²×Q₈	—	2	4	no	—
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×Q₈	—	2	2	no	—
347	C₂²×Q₈	—	2	8	no	—
348	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
349	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
350	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
351	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
352	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
353	C₂²×D₄	—	2	4	no	—
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	—	2	8	no	—
356	C₂²×D₄	—	2	4	no	—
357	C₂²×D₄	D₄×C₁₉	1	2	yes	—
358	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
360	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
361	C₂³×C₄	—	2	4	no	—
362	C₂³×C₄	—	2	2	no	—
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
365	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
366	#137	—	2	32	no	—
367	#137	—	2	32	no	—
368	C₂×Q₁₆	—	2	16	no	—
369	C₂×Q₁₆	C₂³×C₁₉	1	16	yes	—
370	C₂×SD₁₆	—	2	16	no	—
371	C₂×SD₁₆	C₂³×C₁₉	1	16	yes	—
372	C₂×M₁₆	—	2	8	no	—
373	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
374	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
375	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
376	C₄⋊Q₈	—	2	8	no	—
377	#124	—	2	8	no	—
378	#123	—	2	16	no	—
379	C₂²⋊Q₈	—	2	8	no	—
380	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
381	#117	—	2	2	no	—
382	#117	C₂³×C₁₉	1	4	yes	—
383	C₂×C₄⋊C₄	—	2	4	no	—
384	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	4	no	—
387	C₂×C₄²	—	2	1	no	—
388	#103	C₂³×C₁₉	1	16	yes	—
389	#102	C₂³×C₁₉	1	16	yes	—
390	C₂²⋊C₈	C₂³×C₁₉	1	16	yes	—
391	C₁₉	#60370	1	1	yes	characteristic, direct product factor, Sylow
392	C₂⁴	—	2	4	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
395	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
396	#41	—	2	32	no	—
397	#41	—	2	64	no	—
398	#41	—	2	32	no	—
399	#41	—	2	32	no	—
400	#41	—	2	32	no	—
401	#41	—	2	16	no	—
402	#41	—	2	16	no	—
403	#41	—	2	16	no	—
404	#41	—	2	16	no	—
405	#41	—	2	16	no	—
406	#41	—	2	8	no	—
407	#41	—	2	8	no	—
408	#41	—	2	8	no	—
409	#41	—	2	8	no	—
410	#41	C₂×D₄×C₁₉	1	16	yes	—
411	#41	C₂×D₄×C₁₉	1	16	yes	—
412	C₂×Q₈	—	2	32	no	—
413	C₂×Q₈	—	2	16	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	4	no	—
420	C₂×Q₈	—	2	8	no	—
421	C₂×Q₈	—	2	8	no	—
422	C₂×Q₈	—	2	8	no	—
423	C₂×Q₈	—	4	8	no	—
424	C₂×Q₈	—	4	4	no	—
425	C₂×Q₈	C₂×D₄×C₁₉	1	8	yes	—
426	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
427	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
428	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
429	C₂×D₄	—	2	32	no	—
430	C₂×D₄	—	2	64	no	—
431	C₂×D₄	—	2	32	no	—
432	C₂×D₄	—	2	16	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	16	no	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
443	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
444	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
445	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
446	C₂²×C₄	—	2	32	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	16	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	8	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
459	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
460	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
462	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
463	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
464	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
466	Q₁₆	—	2	32	no	—
467	SD₁₆	—	2	32	no	—
468	M₁₆	—	2	8	no	—
469	M₁₆	—	2	8	no	—
470	C₂×C₈	—	2	8	no	—
471	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
472	C₄⋊C₄	—	2	16	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	16	no	—
477	C₄²	—	2	4	no	—
478	C₂³	—	2	16	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	8	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	4	no	—
484	C₂³	—	8	4	no	—
485	C₂³	—	8	8	no	—
486	C₂³	C₁₉×#120	1	4	yes	—
487	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
488	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
489	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
490	Q₈	—	2	16	no	—
491	Q₈	—	2	8	no	—
492	Q₈	—	2	8	no	—
493	Q₈	—	2	4	no	—
494	Q₈	—	2	8	no	—
495	Q₈	—	4	4	no	—
496	Q₈	—	4	8	no	—
497	Q₈	C₂²×D₄×C₁₉	1	8	yes	—
498	D₄	—	2	32	no	—
499	D₄	—	2	16	no	—
500	D₄	—	2	16	no	—
501	D₄	—	2	16	no	—
502	D₄	—	2	16	no	—
503	D₄	—	2	8	no	—
504	D₄	—	2	8	no	—
505	D₄	—	2	4	no	—
506	D₄	C₂²×D₄×C₁₉	1	8	yes	—
507	C₂×C₄	—	2	16	no	—
508	C₂×C₄	—	2	32	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	16	no	—
513	C₂×C₄	—	2	8	no	—
514	C₂×C₄	—	2	16	no	—
515	C₂×C₄	—	2	8	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	C₁₉×#120	1	8	yes	—
522	C₂×C₄	C₁₉×#120	1	4	yes	—
523	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
524	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
525	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
527	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
528	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
529	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
530	C₈	—	2	8	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	2	8	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	8	no	—
538	C₂²	—	8	4	no	—
539	C₂²	—	8	8	no	—
540	C₂²	—	8	16	no	—
541	C₂²	C₂×C₁₉×#120	1	4	yes	—
542	C₂²	C₂×C₁₉×#120	1	2	yes	—
543	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
544	C₄	—	2	8	no	—
545	C₄	—	2	4	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	4	no	—
548	C₄	C₂×C₁₉×#120	1	2	yes	—
549	C₄	C₂×C₁₉×#120	1	4	yes	—
550	C₄	C₂³×D₄×C₁₉	1	2	yes	—
551	C₂	—	2	2	no	—
552	C₂	—	2	4	no	—
553	C₂	—	4	4	no	—
554	C₂	—	4	8	no	—
555	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic
556	C₂	C₁₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
prime radical	C₂×C₁₉×#585	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₉×#137	C₂	semidirect
3. C₂×C₁₉×#536	C₂	semidirect
4. C₁₉×#3011	C₂	semidirect
5. C₁₉×#3009	C₂	semidirect
6. C₁₉×#3007	C₂	semidirect
7. C₁₉×#2896	C₂	semidirect
8. C₁₉×#2879	C₂	semidirect
19. C₂³×Q₈×C₁₉	C₂²	semidirect
21. C₂×C₁₉×#137	C₂²	semidirect
22. C₂×C₁₉×#137	C₂²	semidirect
23. C₂²×Q₁₆×C₁₉	C₂²	semidirect
24. C₂²×SD₁₆×C₁₉	C₂²	semidirect
25. C₂²×M₁₆×C₁₉	C₂²	semidirect
27. C₁₉×#536	C₂²	semidirect
31. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₁₉×#117	C₂²	semidirect
33. C₁₉×#452	C₂²	semidirect
34. C₁₉×#451	C₂²	semidirect
35. C₁₉×#450	C₂²	semidirect
36. C₁₉×#419	C₂²	semidirect
37. C₁₉×#418	C₂²	semidirect
38. C₁₉×#417	C₂²	semidirect
39. C₁₉×#416	C₂²	semidirect
40. C₁₉×#408	C₂²	semidirect
41. C₁₉×#407	C₂²	semidirect
199. #60370	C₁₉	direct (N × H)
254. C₂²×#137	C₂×C₁₉	semidirect
255. C₂×#536	C₂×C₁₉	semidirect
256. #3011	C₂×C₁₉	semidirect
257. #3009	C₂×C₁₉	semidirect
258. #3007	C₂×C₁₉	semidirect
259. #2896	C₂×C₁₉	semidirect
260. #2879	C₂×C₁₉	semidirect
291. C₂³×Q₈	C₂²×C₁₉	semidirect
293. C₂×#137	C₂²×C₁₉	semidirect
294. C₂×#137	C₂²×C₁₉	semidirect
295. C₂²×Q₁₆	C₂²×C₁₉	semidirect
296. C₂²×SD₁₆	C₂²×C₁₉	semidirect
297. C₂²×M₁₆	C₂²×C₁₉	semidirect
299. #536	C₂²×C₁₉	semidirect
303. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
304. C₂×#117	C₂²×C₁₉	semidirect
305. #452	C₂²×C₁₉	semidirect
306. #451	C₂²×C₁₉	semidirect
307. #450	C₂²×C₁₉	semidirect
308. #419	C₂²×C₁₉	semidirect
309. #418	C₂²×C₁₉	semidirect
310. #417	C₂²×C₁₉	semidirect
311. #416	C₂²×C₁₉	semidirect
312. #408	C₂²×C₁₉	semidirect
313. #407	C₂²×C₁₉	semidirect
391. C₁₉	#60370	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×#585	2
C₂²×C₁₉×#137	2
C₂×C₁₉×#536	2
C₁₉×#3011	2
C₁₉×#3009	2
C₁₉×#3007	2
C₁₉×#2896	2
C₁₉×#2879	2
#60370	19

Subgroups — C19×#60370 #18066329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60370 #18066329