Subgroups — C₁₉×#60320 #18066279

Order 4864.

1876 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3483	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2990	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2989	C₂	1	4	yes	maximal, complemented
4	C₁₉×#2981	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2980	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2970	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2965	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2935	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2932	C₂	1	4	yes	maximal, complemented
11	C₁₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#131	C₂²	1	2	yes	—
13	C₂×C₁₉×#131	C₂²	1	4	yes	—
14	Q₈²×C₁₉	C₄	1	1	yes	characteristic
15	C₁₉×#555	C₄	1	4	yes	—
16	C₁₉×#555	C₄	1	1	yes	characteristic
17	C₁₉×#555	C₄	1	4	yes	—
18	C₁₉×#550	C₄	1	2	yes	—
19	C₁₉×#550	C₄	1	4	yes	—
20	C₁₉×#532	C₂²	1	1	yes	characteristic
21	C₁₉×#532	C₂²	1	4	yes	—
22	C₁₉×#532	C₂²	1	4	yes	—
23	C₄×#41×C₁₉	C₂²	1	2	yes	—
24	C₄×#41×C₁₉	C₂²	1	4	yes	—
25	C₁₉×#446	C₂²	1	2	yes	—
26	C₁₉×#446	C₂²	1	2	yes	—
27	C₁₉×#446	C₂²	1	4	yes	—
28	C₁₉×#436	C₂²	1	4	yes	—
29	C₁₉×#436	C₂²	1	2	yes	—
30	C₁₉×#436	C₂²	1	4	yes	—
31	C₁₉×#436	C₂²	1	2	yes	—
32	C₁₉×#435	C₂²	1	4	yes	—
33	C₁₉×#435	C₂²	1	8	yes	—
34	C₁₉×#435	C₂²	1	8	yes	—
35	C₁₉×#435	C₂²	1	8	yes	—
36	C₁₉×#435	C₂²	1	8	yes	—
37	C₁₉×#435	C₂²	1	4	yes	—
38	C₁₉×#435	C₂²	1	8	yes	—
39	C₈×D₄×C₁₉	C₂²	1	4	yes	—
40	C₈×D₄×C₁₉	C₂²	1	4	yes	—
41	C₈×D₄×C₁₉	C₂²	1	4	yes	—
42	C₁₉×#432	C₂²	1	8	yes	—
43	C₁₉×#432	C₂²	1	4	yes	—
44	C₁₉×#431	C₂²	1	2	yes	—
45	C₁₉×#431	C₂²	1	4	yes	—
46	C₁₉×#423	C₂²	1	1	yes	characteristic
47	C₁₉×#423	C₂²	1	4	yes	—
48	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	—
49	C₁₉×#408	C₂²	1	2	yes	—
50	C₁₉×#408	C₂²	1	4	yes	—
51	C₁₉×#408	C₂²	1	4	yes	—
52	C₁₉×#408	C₂²	1	8	yes	—
53	C₄×M₁₆×C₁₉	C₂²	1	4	yes	—
54	C₂×C₁₉×#97	C₂²	1	4	yes	—
55	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
56	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
57	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
58	C₂×#41×C₁₉	C₂³	1	2	yes	—
59	C₂×#41×C₁₉	C₂³	1	4	yes	—
60	C₁₉×#131	—	4	4	no	—
61	C₁₉×#131	—	4	8	no	—
62	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
63	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
64	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
65	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
66	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
67	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
71	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
72	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
73	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
74	C₁₉×C₄⋊Q₈	C₂×C₄	1	4	yes	—
75	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
76	C₁₉×#127	C₂×C₄	1	4	yes	—
77	C₁₉×#127	C₂×C₄	1	4	yes	—
78	C₁₉×#124	C₂×C₄	1	2	yes	—
79	C₁₉×#124	C₂×C₄	1	4	yes	—
80	C₁₉×#124	C₂×C₄	1	4	yes	—
81	C₁₉×#124	C₂×C₄	1	8	yes	—
82	C₁₉×#121	C₂×C₄	1	4	yes	—
83	C₁₉×#121	C₂×C₄	1	4	yes	—
84	C₁₉×#121	C₂×C₄	1	4	yes	—
85	C₁₉×#121	C₂×C₄	1	8	yes	—
86	C₁₉×#121	C₂×C₄	1	8	yes	—
87	C₁₉×#121	C₂×C₄	1	8	yes	—
88	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
89	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
90	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
91	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
92	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
93	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
94	C₄×D₄×C₁₉	C₂×C₄	1	8	yes	—
95	C₄×D₄×C₁₉	C₂³	1	4	yes	—
96	C₄×D₄×C₁₉	C₂³	1	2	yes	—
97	C₄×D₄×C₁₉	C₂³	1	4	yes	—
98	C₄×D₄×C₁₉	C₂³	1	8	yes	—
99	C₁₉×#117	C₂×C₄	1	2	yes	—
100	C₁₉×#117	C₂×C₄	1	4	yes	—
101	C₁₉×#117	C₂×C₄	1	4	yes	—
102	C₁₉×#117	C₂×C₄	1	8	yes	—
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
105	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
106	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
107	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
108	C₁₉×C₄⋊C₈	C₂³	1	8	yes	—
109	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
110	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
111	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
112	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
113	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
114	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
115	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
116	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
117	C₁₉×C₂²⋊C₈	C₂³	1	8	yes	—
118	C₁₉×#97	C₂³	1	4	yes	—
119	C₁₉×#97	C₂³	1	8	yes	—
120	C₁₉×#97	C₂³	1	4	yes	—
121	C₄×C₈×C₁₉	C₂³	1	2	yes	—
122	C₄×C₈×C₁₉	C₂³	1	2	yes	—
123	C₄×C₈×C₁₉	C₂³	1	4	yes	—
124	#41×C₁₉	—	4	2	no	—
125	#41×C₁₉	—	4	4	no	—
126	#41×C₁₉	—	4	2	no	—
127	#41×C₁₉	—	4	4	no	—
128	#41×C₁₉	—	4	4	no	—
129	#41×C₁₉	—	4	8	no	—
130	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
131	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
132	C₂×Q₈×C₁₉	C₂²×C₄	1	4	yes	—
133	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
134	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
135	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
136	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
137	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
138	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
139	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
140	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
144	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
148	M₁₆×C₁₉	—	2	8	no	—
149	M₁₆×C₁₉	—	4	4	no	—
150	M₁₆×C₁₉	—	4	2	no	—
151	M₁₆×C₁₉	—	4	4	no	—
152	M₁₆×C₁₉	—	4	4	no	—
153	C₂×C₈×C₁₉	—	2	8	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	4	4	no	—
156	C₂×C₈×C₁₉	—	4	1	no	—
157	C₂×C₈×C₁₉	—	4	8	no	—
158	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
159	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
160	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
161	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
162	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
163	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
165	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
166	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
167	C₄⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
168	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
170	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
171	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
172	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
173	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
174	C₂²⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
175	C₂²⋊C₄×C₁₉	C₂²×C₄	1	8	yes	—
176	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
178	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
179	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
180	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
181	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₁₉	C₂⁴	1	2	yes	—
183	C₄²×C₁₉	C₂⁴	1	4	yes	—
184	#60320	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
186	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
187	C₂³×C₁₉	C₂³×C₄	1	4	yes	—
188	Q₈×C₁₉	—	2	4	no	—
189	Q₈×C₁₉	—	4	2	no	—
190	Q₈×C₁₉	—	4	4	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	2	8	no	—
193	D₄×C₁₉	—	4	4	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	4	no	—
196	D₄×C₁₉	—	4	8	no	—
197	D₄×C₁₉	—	4	4	no	—
198	D₄×C₁₉	—	4	8	no	—
199	C₂×C₄×C₁₉	—	2	4	no	—
200	C₂×C₄×C₁₉	—	2	8	no	—
201	C₂×C₄×C₁₉	—	2	4	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	4	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	4	no	—
207	C₂×C₄×C₁₉	—	4	8	no	—
208	C₂×C₄×C₁₉	—	4	4	no	—
209	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
210	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
211	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
212	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
214	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
215	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
216	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
217	C₈×C₁₉	—	2	4	no	—
218	C₈×C₁₉	—	2	1	no	—
219	C₈×C₁₉	—	2	4	no	—
220	C₈×C₁₉	—	2	4	no	—
221	C₈×C₁₉	—	2	2	no	—
222	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
223	#3483	C₂×C₁₉	1	1	yes	characteristic
224	#2990	C₂×C₁₉	1	2	yes	complemented
225	#2989	C₂×C₁₉	1	4	yes	complemented
226	#2981	C₂×C₁₉	1	4	yes	complemented
227	#2980	C₂×C₁₉	1	4	yes	complemented
228	#2979	C₂×C₁₉	1	1	yes	characteristic, complemented
229	#2970	C₂×C₁₉	1	4	yes	complemented
230	#2965	C₂×C₁₉	1	2	yes	complemented
231	#2935	C₂×C₁₉	1	4	yes	complemented
232	#2932	C₂×C₁₉	1	4	yes	complemented
233	#2931	C₂×C₁₉	1	1	yes	characteristic, complemented
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	4	no	—
236	C₂²×C₁₉	—	2	4	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	4	no	—
239	C₂²×C₁₉	—	2	4	no	—
240	C₂²×C₁₉	—	2	8	no	—
241	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
242	C₄×C₁₉	—	2	4	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	2	4	no	—
245	C₄×C₁₉	—	2	2	no	—
246	C₄×C₁₉	—	2	4	no	—
247	C₄×C₁₉	—	2	4	no	—
248	C₄×C₁₉	#568	1	4	yes	—
249	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
250	C₄×C₁₉	#585	1	1	yes	characteristic
251	C₂×#131	C₂²×C₁₉	1	2	yes	—
252	C₂×#131	C₂²×C₁₉	1	4	yes	—
253	Q₈²	C₄×C₁₉	1	1	yes	characteristic
254	#555	C₄×C₁₉	1	4	yes	—
255	#555	C₄×C₁₉	1	1	yes	characteristic
256	#555	C₄×C₁₉	1	4	yes	—
257	#550	C₄×C₁₉	1	2	yes	—
258	#550	C₄×C₁₉	1	4	yes	—
259	#532	C₂²×C₁₉	1	1	yes	characteristic
260	#532	C₂²×C₁₉	1	4	yes	—
261	#532	C₂²×C₁₉	1	4	yes	—
262	C₄×#41	C₂²×C₁₉	1	2	yes	—
263	C₄×#41	C₂²×C₁₉	1	4	yes	—
264	#446	C₂²×C₁₉	1	2	yes	—
265	#446	C₂²×C₁₉	1	2	yes	—
266	#446	C₂²×C₁₉	1	4	yes	—
267	#436	C₂²×C₁₉	1	4	yes	—
268	#436	C₂²×C₁₉	1	2	yes	—
269	#436	C₂²×C₁₉	1	4	yes	—
270	#436	C₂²×C₁₉	1	2	yes	—
271	#435	C₂²×C₁₉	1	4	yes	—
272	#435	C₂²×C₁₉	1	8	yes	—
273	#435	C₂²×C₁₉	1	8	yes	—
274	#435	C₂²×C₁₉	1	8	yes	—
275	#435	C₂²×C₁₉	1	8	yes	—
276	#435	C₂²×C₁₉	1	4	yes	—
277	#435	C₂²×C₁₉	1	8	yes	—
278	C₈×D₄	C₂²×C₁₉	1	4	yes	—
279	C₈×D₄	C₂²×C₁₉	1	4	yes	—
280	C₈×D₄	C₂²×C₁₉	1	4	yes	—
281	#432	C₂²×C₁₉	1	8	yes	—
282	#432	C₂²×C₁₉	1	4	yes	—
283	#431	C₂²×C₁₉	1	2	yes	—
284	#431	C₂²×C₁₉	1	4	yes	—
285	#423	C₂²×C₁₉	1	1	yes	characteristic
286	#423	C₂²×C₁₉	1	4	yes	—
287	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	—
288	#408	C₂²×C₁₉	1	2	yes	—
289	#408	C₂²×C₁₉	1	4	yes	—
290	#408	C₂²×C₁₉	1	4	yes	—
291	#408	C₂²×C₁₉	1	8	yes	—
292	C₄×M₁₆	C₂²×C₁₉	1	4	yes	—
293	C₂×#97	C₂²×C₁₉	1	4	yes	—
294	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×C₁₉	—	4	1	no	—
296	C₂×C₁₉	—	4	4	no	—
297	C₂×C₁₉	—	4	4	no	—
298	C₂×C₁₉	C₄×H(5,𝔽₂)	1	1	yes	characteristic
299	C₂×C₁₉	C₂×#568	1	2	yes	—
300	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
301	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
302	C₂×#41	C₂³×C₁₉	1	2	yes	—
303	C₂×#41	C₂³×C₁₉	1	4	yes	—
304	#131	—	4	4	no	—
305	#131	—	4	8	no	—
306	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
307	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
308	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
309	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
310	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
311	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
313	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
314	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
316	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
317	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
318	C₄⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
319	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
320	#127	C₂×C₄×C₁₉	1	4	yes	—
321	#127	C₂×C₄×C₁₉	1	4	yes	—
322	#124	C₂×C₄×C₁₉	1	2	yes	—
323	#124	C₂×C₄×C₁₉	1	4	yes	—
324	#124	C₂×C₄×C₁₉	1	4	yes	—
325	#124	C₂×C₄×C₁₉	1	8	yes	—
326	#121	C₂×C₄×C₁₉	1	4	yes	—
327	#121	C₂×C₄×C₁₉	1	4	yes	—
328	#121	C₂×C₄×C₁₉	1	4	yes	—
329	#121	C₂×C₄×C₁₉	1	8	yes	—
330	#121	C₂×C₄×C₁₉	1	8	yes	—
331	#121	C₂×C₄×C₁₉	1	8	yes	—
332	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
333	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
334	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
335	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
336	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
337	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
338	C₄×D₄	C₂×C₄×C₁₉	1	8	yes	—
339	C₄×D₄	C₂³×C₁₉	1	2	yes	—
340	C₄×D₄	C₂³×C₁₉	1	4	yes	—
341	C₄×D₄	C₂³×C₁₉	1	4	yes	—
342	C₄×D₄	C₂³×C₁₉	1	8	yes	—
343	#117	C₂×C₄×C₁₉	1	2	yes	—
344	#117	C₂×C₄×C₁₉	1	4	yes	—
345	#117	C₂×C₄×C₁₉	1	4	yes	—
346	#117	C₂×C₄×C₁₉	1	8	yes	—
347	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
349	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
350	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
351	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
352	C₄⋊C₈	C₂³×C₁₉	1	8	yes	—
353	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
354	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
355	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
356	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
357	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
358	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
359	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
360	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
361	C₂²⋊C₈	C₂³×C₁₉	1	8	yes	—
362	#97	C₂³×C₁₉	1	4	yes	—
363	#97	C₂³×C₁₉	1	8	yes	—
364	#97	C₂³×C₁₉	1	4	yes	—
365	C₄×C₈	C₂³×C₁₉	1	2	yes	—
366	C₄×C₈	C₂³×C₁₉	1	2	yes	—
367	C₄×C₈	C₂³×C₁₉	1	4	yes	—
368	C₁₉	#60320	1	1	yes	characteristic, direct product factor, Sylow
369	#41	—	4	2	no	—
370	#41	—	4	4	no	—
371	#41	—	4	2	no	—
372	#41	—	4	4	no	—
373	#41	—	4	4	no	—
374	#41	—	4	8	no	—
375	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
376	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
377	C₂×Q₈	C₂²×C₄×C₁₉	1	4	yes	—
378	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
379	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
380	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
381	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
382	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
383	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
384	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
385	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
386	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
387	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
388	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
389	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
390	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
393	M₁₆	—	2	8	no	—
394	M₁₆	—	4	4	no	—
395	M₁₆	—	4	2	no	—
396	M₁₆	—	4	4	no	—
397	M₁₆	—	4	4	no	—
398	C₂×C₈	—	2	8	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	4	4	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	8	no	—
403	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
404	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
405	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
406	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
407	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
408	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
409	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
410	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
411	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
412	C₄⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
413	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
414	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
415	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
416	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
417	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
418	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
419	C₂²⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
420	C₂²⋊C₄	C₂²×C₄×C₁₉	1	8	yes	—
421	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
422	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
423	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
424	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
425	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
426	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
427	C₄²	C₂⁴×C₁₉	1	2	yes	—
428	C₄²	C₂⁴×C₁₉	1	4	yes	—
429	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
430	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
431	C₂³	C₂³×C₄×C₁₉	1	4	yes	—
432	Q₈	—	2	4	no	—
433	Q₈	—	4	2	no	—
434	Q₈	—	4	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	2	8	no	—
437	D₄	—	4	4	no	—
438	D₄	—	4	2	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	8	no	—
441	D₄	—	4	4	no	—
442	D₄	—	4	8	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
454	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
455	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
456	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
457	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
458	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
459	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
460	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
461	C₈	—	2	4	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	4	no	—
464	C₈	—	2	4	no	—
465	C₈	—	2	2	no	—
466	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	8	no	—
474	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	4	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	4	no	—
480	C₄	—	2	4	no	—
481	C₄	C₁₉×#568	1	4	yes	—
482	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
483	C₄	C₁₉×#585	1	1	yes	characteristic
484	C₂	—	4	1	no	—
485	C₂	—	4	4	no	—
486	C₂	—	4	4	no	—
487	C₂	C₄×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂	C₂×C₁₉×#568	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂⁴×C₄
prime radical	C₁₉×#3483	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2990	C₂	semidirect
3. C₁₉×#2989	C₂	semidirect
4. C₁₉×#2981	C₂	semidirect
5. C₁₉×#2980	C₂	semidirect
6. C₁₉×#2979	C₂	semidirect
7. C₁₉×#2970	C₂	semidirect
8. C₁₉×#2965	C₂	semidirect
9. C₁₉×#2935	C₂	semidirect
10. C₁₉×#2932	C₂	semidirect
11. C₁₉×#2931	C₂	semidirect
184. #60320	C₁₉	direct (N × H)
224. #2990	C₂×C₁₉	semidirect
225. #2989	C₂×C₁₉	semidirect
226. #2981	C₂×C₁₉	semidirect
227. #2980	C₂×C₁₉	semidirect
228. #2979	C₂×C₁₉	semidirect
229. #2970	C₂×C₁₉	semidirect
230. #2965	C₂×C₁₉	semidirect
231. #2935	C₂×C₁₉	semidirect
232. #2932	C₂×C₁₉	semidirect
233. #2931	C₂×C₁₉	semidirect
368. C₁₉	#60320	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×#3483	2
C₁₉×#2990	2
C₁₉×#2989	2
C₁₉×#2981	2
C₁₉×#2980	2
C₁₉×#2979	2
C₁₉×#2970	2
C₁₉×#2965	2
C₁₉×#2935	2
C₁₉×#2932	2
C₁₉×#2931	2
#60320	19

Subgroups — C19×#60320 #18066279

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60320 #18066279