Subgroups — C₁₉×#62273 #18068232

Order 4864.

1820 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3540	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3340	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3319	C₂	1	4	yes	maximal, complemented
4	C₁₉×#3313	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3282	C₂	1	4	yes	maximal, complemented
6	C₁₉×#3262	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3202	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#3199	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#3197	C₂	1	2	yes	maximal, complemented
10	C₁₉×#3173	C₂	1	2	yes	maximal, complemented
11	C₁₉×#3057	C₂	1	2	yes	maximal, complemented
12	C₁₉×#3050	C₂	1	2	yes	maximal, complemented
13	C₁₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉×#135	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
16	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×H(3,𝔽₄)	—	2	2	no	—
19	C₁₉×#560	—	2	2	no	—
20	C₁₉×#559	—	2	2	no	—
21	C₁₉×#556	C₂²	1	4	yes	complemented
22	C₁₉×#555	C₂²	1	4	yes	—
23	C₁₉×#551	—	2	2	no	—
24	C₁₉×#548	C₂²	1	4	yes	—
25	C₁₉×#546	C₂²	1	4	yes	complemented
26	C₁₉×#542	—	2	4	no	—
27	C₁₉×#542	C₂²	1	4	yes	complemented
28	C₁₉×#538	—	2	4	no	—
29	C₁₉×#536	C₂²	1	2	yes	—
30	C₁₉×#535	C₂²	1	2	yes	—
31	C₁₉×#525	C₂²	1	1	yes	characteristic
32	C₁₉×#525	C₂²	1	4	yes	complemented
33	C₁₉×#498	C₂²	1	2	yes	complemented
34	C₁₉×#495	C₂²	1	2	yes	complemented
35	C₁₉×#489	C₂²	1	4	yes	complemented
36	C₁₉×#485	C₂²	1	4	yes	complemented
37	C₁₉×#485	C₂²	1	4	yes	complemented
38	C₁₉×#482	C₂²	1	4	yes	complemented
39	C₁₉×#482	C₂²	1	4	yes	complemented
40	C₁₉×#477	C₂²	1	4	yes	complemented
41	C₁₉×#474	C₂²	1	4	yes	complemented
42	C₁₉×#470	C₂²	1	2	yes	complemented
43	C₁₉×#469	C₂²	1	2	yes	—
44	C₁₉×#468	C₂²	1	4	yes	complemented
45	C₁₉×#468	C₂²	1	4	yes	complemented
46	C₁₉×#467	C₂²	1	2	yes	complemented
47	C₁₉×#467	C₂²	1	2	yes	complemented
48	C₁₉×#466	C₂²	1	2	yes	—
49	C₁₉×#466	C₂²	1	2	yes	—
50	C₁₉×#465	C₂²	1	4	yes	complemented
51	C₁₉×#465	C₂²	1	4	yes	complemented
52	C₁₉×#465	C₂²	1	4	yes	complemented
53	C₁₉×#464	C₂²	1	4	yes	complemented
54	C₁₉×#463	C₂²	1	4	yes	complemented
55	C₁₉×#452	C₂²	1	4	yes	complemented
56	C₁₉×#451	C₂²	1	4	yes	complemented
57	C₁₉×#449	C₂²	1	4	yes	—
58	C₁₉×#447	C₂²	1	4	yes	complemented
59	C₁₉×#442	C₂²	1	2	yes	complemented
60	C₁₉×#441	C₂²	1	2	yes	complemented
61	C₄×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
62	C₁₉×#435	C₂²	1	4	yes	complemented
63	C₈×D₄×C₁₉	C₂²	1	4	yes	complemented
64	C₁₉×#427	C₂²	1	2	yes	complemented
65	C₁₉×#427	C₂²	1	2	yes	complemented
66	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
67	C₁₉×#419	C₂²	1	2	yes	complemented
68	C₁₉×#418	C₂²	1	2	yes	complemented
69	C₁₉×#416	C₂²	1	4	yes	complemented
70	C₁₉×#408	C₂²	1	1	yes	characteristic
71	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
72	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
73	C₂×#41×C₁₉	C₂³	1	4	yes	—
74	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₁₉×#135	—	4	4	no	—
79	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
80	C₂×Q₁₆×C₁₉	C₂³	1	2	yes	—
81	C₂×SD₁₆×C₁₉	—	4	4	no	—
82	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
83	C₂×SD₁₆×C₁₉	C₂³	1	4	yes	—
84	C₂×D₈×C₁₉	C₂³	1	2	yes	—
85	C₂×D₈×C₁₉	C₂³	1	2	yes	—
86	C₁₉×#131	—	4	2	no	—
87	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
90	C₂²×C₈×C₁₉	—	4	2	no	—
91	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
93	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
96	C₁₉×C₄⋊Q₈	—	2	2	no	—
97	C₁₉×C₄⋊Q₈	C₂³	1	4	yes	—
98	C₁₉×#127	—	2	2	no	—
99	C₁₉×#126	—	2	4	no	—
100	C₁₉×#126	—	2	4	no	—
101	C₁₉×#126	—	2	4	no	—
102	C₁₉×#124	—	2	2	no	—
103	C₁₉×#124	—	2	2	no	—
104	C₁₉×#124	—	2	4	no	—
105	C₁₉×#124	—	2	4	no	—
106	C₁₉×#124	—	2	4	no	—
107	C₁₉×#124	—	2	4	no	—
108	C₁₉×#124	—	2	4	no	—
109	C₁₉×#124	C₂³	1	4	yes	—
110	C₁₉×#123	—	2	2	no	—
111	C₁₉×#123	—	2	2	no	—
112	C₁₉×#123	—	2	4	no	—
113	C₁₉×#123	—	2	4	no	—
114	C₁₉×#123	—	2	4	no	—
115	C₁₉×#123	D₄	1	2	yes	—
116	C₁₉×C₂²⋊Q₈	—	2	4	no	—
117	C₁₉×C₂²⋊Q₈	—	2	4	no	—
118	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
119	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
120	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
121	C₁₉×C₂²⋊Q₈	C₂³	1	4	yes	—
122	C₁₉×#121	—	2	4	no	—
123	C₁₉×#121	—	2	4	no	—
124	C₁₉×#121	—	2	4	no	—
125	C₁₉×#121	D₄	1	2	yes	—
126	C₁₉×#121	C₂³	1	4	yes	—
127	C₁₉×#121	C₂³	1	4	yes	—
128	C₁₉×#121	C₂³	1	4	yes	—
129	C₁₉×#120	—	2	4	no	—
130	C₁₉×#120	—	2	2	no	—
131	C₁₉×#120	—	2	2	no	—
132	C₁₉×#120	—	2	4	no	—
133	C₁₉×#120	D₄	1	2	yes	—
134	C₄×Q₈×C₁₉	—	2	4	no	—
135	C₄×Q₈×C₁₉	C₂³	1	4	yes	—
136	C₄×D₄×C₁₉	—	2	4	no	—
137	C₄×D₄×C₁₉	—	2	4	no	—
138	C₄×D₄×C₁₉	—	2	4	no	—
139	C₄×D₄×C₁₉	C₂³	1	4	yes	—
140	C₄×D₄×C₁₉	C₂³	1	4	yes	—
141	C₁₉×#117	—	2	4	no	—
142	C₁₉×#117	C₂³	1	4	yes	—
143	C₁₉×#117	C₂³	1	2	yes	—
144	C₁₉×#117	C₂³	1	2	yes	—
145	C₁₉×#117	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₁₉×#107	C₂³	1	2	yes	—
148	C₁₉×#107	C₂³	1	2	yes	—
149	C₁₉×#107	C₂³	1	4	yes	—
150	C₁₉×#106	C₂³	1	4	yes	—
151	C₁₉×#106	C₂³	1	2	yes	—
152	C₁₉×#106	C₂³	1	2	yes	—
153	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
154	C₁₉×#103	C₂³	1	4	yes	—
155	C₁₉×#103	C₂³	1	4	yes	—
156	C₁₉×#103	C₂³	1	4	yes	—
157	C₁₉×#103	C₂³	1	4	yes	—
158	C₁₉×#102	C₂³	1	4	yes	—
159	C₁₉×#102	C₂³	1	4	yes	—
160	C₁₉×#102	C₂³	1	4	yes	—
161	C₁₉×#102	C₂³	1	4	yes	—
162	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
163	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₁₉×#97	C₂³	1	2	yes	—
165	C₄×C₈×C₁₉	C₂³	1	2	yes	—
166	C₂⁴×C₁₉	—	2	2	no	—
167	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
168	#41×C₁₉	—	4	1	no	—
169	#41×C₁₉	—	4	1	no	—
170	#41×C₁₉	—	4	4	no	—
171	#41×C₁₉	—	4	4	no	—
172	C₂×Q₈×C₁₉	—	2	4	no	—
173	C₂×Q₈×C₁₉	—	2	2	no	—
174	C₂×Q₈×C₁₉	—	4	2	no	—
175	C₂×Q₈×C₁₉	—	4	2	no	—
176	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
178	C₂×D₄×C₁₉	—	2	4	no	—
179	C₂×D₄×C₁₉	—	2	4	no	—
180	C₂×D₄×C₁₉	—	2	4	no	—
181	C₂×D₄×C₁₉	—	2	4	no	—
182	C₂×D₄×C₁₉	—	2	2	no	—
183	C₂×D₄×C₁₉	—	4	2	no	—
184	C₂×D₄×C₁₉	—	4	2	no	—
185	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
186	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₁₉	—	2	2	no	—
190	C₂²×C₄×C₁₉	—	2	4	no	—
191	C₂²×C₄×C₁₉	—	2	4	no	—
192	C₂²×C₄×C₁₉	—	4	1	no	—
193	C₂²×C₄×C₁₉	—	4	1	no	—
194	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
199	Q₁₆×C₁₉	—	4	2	no	—
200	Q₁₆×C₁₉	—	4	2	no	—
201	SD₁₆×C₁₉	—	2	8	no	—
202	SD₁₆×C₁₉	—	4	4	no	—
203	D₈×C₁₉	—	4	2	no	—
204	D₈×C₁₉	—	4	2	no	—
205	M₁₆×C₁₉	—	4	1	no	—
206	M₁₆×C₁₉	—	4	2	no	—
207	M₁₆×C₁₉	—	4	1	no	—
208	C₂×C₈×C₁₉	—	2	2	no	—
209	C₂×C₈×C₁₉	—	2	4	no	—
210	C₂×C₈×C₁₉	—	2	4	no	—
211	C₂×C₈×C₁₉	—	4	2	no	—
212	C₂×C₈×C₁₉	—	4	1	no	—
213	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
214	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
215	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
216	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
217	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
218	C₄⋊C₄×C₁₉	—	2	4	no	—
219	C₄⋊C₄×C₁₉	—	2	4	no	—
220	C₄⋊C₄×C₁₉	—	2	4	no	—
221	C₄⋊C₄×C₁₉	—	2	4	no	—
222	C₄⋊C₄×C₁₉	—	2	4	no	—
223	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
224	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
225	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
226	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
227	C₂²⋊C₄×C₁₉	—	2	4	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₉	—	2	4	no	—
230	C₂²⋊C₄×C₁₉	—	2	2	no	—
231	C₂²⋊C₄×C₁₉	—	2	4	no	—
232	C₂²⋊C₄×C₁₉	—	2	4	no	—
233	C₂²⋊C₄×C₁₉	—	2	4	no	—
234	C₂²⋊C₄×C₁₉	—	2	4	no	—
235	C₂²⋊C₄×C₁₉	—	2	4	no	—
236	C₂²⋊C₄×C₁₉	—	2	4	no	—
237	C₂²⋊C₄×C₁₉	—	2	4	no	—
238	C₂²⋊C₄×C₁₉	—	2	4	no	—
239	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
240	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
241	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
242	C₄²×C₁₉	—	2	2	no	—
243	C₄²×C₁₉	—	2	4	no	—
244	C₄²×C₁₉	—	2	2	no	—
245	C₄²×C₁₉	—	2	4	no	—
246	C₄²×C₁₉	C₂⁴	1	2	yes	—
247	#62273	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂³×C₁₉	—	2	4	no	—
249	C₂³×C₁₉	—	4	1	no	—
250	C₂³×C₁₉	—	4	2	no	—
251	C₂³×C₁₉	—	8	2	no	—
252	C₂³×C₁₉	—	8	4	no	—
253	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
254	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
255	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
256	Q₈×C₁₉	—	2	4	no	—
257	Q₈×C₁₉	—	2	4	no	—
258	Q₈×C₁₉	—	4	1	no	—
259	Q₈×C₁₉	—	8	4	no	—
260	Q₈×C₁₉	—	8	2	no	—
261	D₄×C₁₉	—	2	4	no	—
262	D₄×C₁₉	—	2	4	no	—
263	D₄×C₁₉	—	4	4	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	4	2	no	—
266	D₄×C₁₉	—	8	2	no	—
267	D₄×C₁₉	—	8	4	no	—
268	D₄×C₁₉	—	8	4	no	—
269	D₄×C₁₉	—	8	4	no	—
270	D₄×C₁₉	—	8	4	no	—
271	C₂×C₄×C₁₉	—	2	1	no	—
272	C₂×C₄×C₁₉	—	2	2	no	—
273	C₂×C₄×C₁₉	—	2	2	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	4	no	—
278	C₂×C₄×C₁₉	—	2	4	no	—
279	C₂×C₄×C₁₉	—	2	4	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	2	no	—
282	C₂×C₄×C₁₉	—	8	4	no	—
283	C₂×C₄×C₁₉	—	8	4	no	—
284	C₂×C₄×C₁₉	—	8	2	no	—
285	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
288	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
290	C₈×C₁₉	—	2	1	no	—
291	C₈×C₁₉	—	2	2	no	—
292	C₈×C₁₉	—	2	2	no	—
293	C₈×C₁₉	—	2	2	no	—
294	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
295	#3540	C₂×C₁₉	1	2	yes	complemented
296	#3340	C₂×C₁₉	1	4	yes	complemented
297	#3319	C₂×C₁₉	1	4	yes	complemented
298	#3313	C₂×C₁₉	1	4	yes	complemented
299	#3282	C₂×C₁₉	1	4	yes	complemented
300	#3262	C₂×C₁₉	1	2	yes	complemented
301	#3202	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#3199	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#3197	C₂×C₁₉	1	2	yes	complemented
304	#3173	C₂×C₁₉	1	2	yes	complemented
305	#3057	C₂×C₁₉	1	2	yes	complemented
306	#3050	C₂×C₁₉	1	2	yes	complemented
307	#2929	C₂×C₁₉	1	1	yes	characteristic, complemented
308	C₂²×C₁₉	—	2	2	no	—
309	C₂²×C₁₉	—	2	4	no	—
310	C₂²×C₁₉	—	2	2	no	—
311	C₂²×C₁₉	—	2	2	no	—
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	2	2	no	—
314	C₂²×C₁₉	—	2	2	no	—
315	C₂²×C₁₉	—	4	4	no	—
316	C₂²×C₁₉	—	4	4	no	—
317	C₂²×C₁₉	—	4	4	no	—
318	C₂²×C₁₉	—	4	4	no	—
319	C₂²×C₁₉	—	16	4	no	—
320	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
321	C₄×C₁₉	—	2	4	no	—
322	C₄×C₁₉	—	2	2	no	—
323	C₄×C₁₉	—	2	1	no	—
324	C₄×C₁₉	—	2	2	no	—
325	C₄×C₁₉	—	4	4	no	—
326	C₄×C₁₉	—	4	4	no	—
327	C₄×C₁₉	—	4	4	no	—
328	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
329	C₄×C₁₉	#585	1	1	yes	characteristic
330	C₂×#135	C₂²×C₁₉	1	2	yes	—
331	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	complemented
332	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic
333	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
334	H(3,𝔽₄)	—	2	2	no	—
335	#560	—	2	2	no	—
336	#559	—	2	2	no	—
337	#556	C₂²×C₁₉	1	4	yes	complemented
338	#555	C₂²×C₁₉	1	4	yes	—
339	#551	—	2	2	no	—
340	#548	C₂²×C₁₉	1	4	yes	—
341	#546	C₂²×C₁₉	1	4	yes	complemented
342	#542	—	2	4	no	—
343	#542	C₂²×C₁₉	1	4	yes	complemented
344	#538	—	2	4	no	—
345	#536	C₂²×C₁₉	1	2	yes	—
346	#535	C₂²×C₁₉	1	2	yes	—
347	#525	C₂²×C₁₉	1	1	yes	characteristic
348	#525	C₂²×C₁₉	1	4	yes	complemented
349	#498	C₂²×C₁₉	1	2	yes	complemented
350	#495	C₂²×C₁₉	1	2	yes	complemented
351	#489	C₂²×C₁₉	1	4	yes	complemented
352	#485	C₂²×C₁₉	1	4	yes	complemented
353	#485	C₂²×C₁₉	1	4	yes	complemented
354	#482	C₂²×C₁₉	1	4	yes	complemented
355	#482	C₂²×C₁₉	1	4	yes	complemented
356	#477	C₂²×C₁₉	1	4	yes	complemented
357	#474	C₂²×C₁₉	1	4	yes	complemented
358	#470	C₂²×C₁₉	1	2	yes	complemented
359	#469	C₂²×C₁₉	1	2	yes	—
360	#468	C₂²×C₁₉	1	4	yes	complemented
361	#468	C₂²×C₁₉	1	4	yes	complemented
362	#467	C₂²×C₁₉	1	2	yes	complemented
363	#467	C₂²×C₁₉	1	2	yes	complemented
364	#466	C₂²×C₁₉	1	2	yes	—
365	#466	C₂²×C₁₉	1	2	yes	—
366	#465	C₂²×C₁₉	1	4	yes	complemented
367	#465	C₂²×C₁₉	1	4	yes	complemented
368	#465	C₂²×C₁₉	1	4	yes	complemented
369	#464	C₂²×C₁₉	1	4	yes	complemented
370	#463	C₂²×C₁₉	1	4	yes	complemented
371	#452	C₂²×C₁₉	1	4	yes	complemented
372	#451	C₂²×C₁₉	1	4	yes	complemented
373	#449	C₂²×C₁₉	1	4	yes	—
374	#447	C₂²×C₁₉	1	4	yes	complemented
375	#442	C₂²×C₁₉	1	2	yes	complemented
376	#441	C₂²×C₁₉	1	2	yes	complemented
377	C₄×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
378	#435	C₂²×C₁₉	1	4	yes	complemented
379	C₈×D₄	C₂²×C₁₉	1	4	yes	complemented
380	#427	C₂²×C₁₉	1	2	yes	complemented
381	#427	C₂²×C₁₉	1	2	yes	complemented
382	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
383	#419	C₂²×C₁₉	1	2	yes	complemented
384	#418	C₂²×C₁₉	1	2	yes	complemented
385	#416	C₂²×C₁₉	1	4	yes	complemented
386	#408	C₂²×C₁₉	1	1	yes	characteristic
387	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
388	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
389	C₂×C₁₉	—	4	2	no	—
390	C₂×C₁₉	—	4	1	no	—
391	C₂×C₁₉	—	4	2	no	—
392	C₂×C₁₉	—	8	4	no	—
393	C₂×C₁₉	#3496	1	1	yes	characteristic
394	C₂×C₁₉	#3584	1	2	yes	—
395	C₂×#41	C₂³×C₁₉	1	4	yes	—
396	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
397	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
398	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
399	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
400	#135	—	4	4	no	—
401	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
402	C₂×Q₁₆	C₂³×C₁₉	1	2	yes	—
403	C₂×SD₁₆	—	4	4	no	—
404	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
405	C₂×SD₁₆	C₂³×C₁₉	1	4	yes	—
406	C₂×D₈	C₂³×C₁₉	1	2	yes	—
407	C₂×D₈	C₂³×C₁₉	1	2	yes	—
408	#131	—	4	2	no	—
409	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
410	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
411	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
412	C₂²×C₈	—	4	2	no	—
413	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
415	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
416	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
418	C₄⋊Q₈	—	2	2	no	—
419	C₄⋊Q₈	C₂³×C₁₉	1	4	yes	—
420	#127	—	2	2	no	—
421	#126	—	2	4	no	—
422	#126	—	2	4	no	—
423	#126	—	2	4	no	—
424	#124	—	2	2	no	—
425	#124	—	2	2	no	—
426	#124	—	2	4	no	—
427	#124	—	2	4	no	—
428	#124	—	2	4	no	—
429	#124	—	2	4	no	—
430	#124	—	2	4	no	—
431	#124	C₂³×C₁₉	1	4	yes	—
432	#123	—	2	2	no	—
433	#123	—	2	2	no	—
434	#123	—	2	4	no	—
435	#123	—	2	4	no	—
436	#123	—	2	4	no	—
437	#123	D₄×C₁₉	1	2	yes	—
438	C₂²⋊Q₈	—	2	4	no	—
439	C₂²⋊Q₈	—	2	4	no	—
440	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
441	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
442	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
443	C₂²⋊Q₈	C₂³×C₁₉	1	4	yes	—
444	#121	—	2	4	no	—
445	#121	—	2	4	no	—
446	#121	—	2	4	no	—
447	#121	D₄×C₁₉	1	2	yes	—
448	#121	C₂³×C₁₉	1	4	yes	—
449	#121	C₂³×C₁₉	1	4	yes	—
450	#121	C₂³×C₁₉	1	4	yes	—
451	#120	—	2	4	no	—
452	#120	—	2	2	no	—
453	#120	—	2	2	no	—
454	#120	—	2	4	no	—
455	#120	D₄×C₁₉	1	2	yes	—
456	C₄×Q₈	—	2	4	no	—
457	C₄×Q₈	C₂³×C₁₉	1	4	yes	—
458	C₄×D₄	—	2	4	no	—
459	C₄×D₄	—	2	4	no	—
460	C₄×D₄	—	2	4	no	—
461	C₄×D₄	C₂³×C₁₉	1	4	yes	—
462	C₄×D₄	C₂³×C₁₉	1	4	yes	—
463	#117	—	2	4	no	—
464	#117	C₂³×C₁₉	1	4	yes	—
465	#117	C₂³×C₁₉	1	2	yes	—
466	#117	C₂³×C₁₉	1	2	yes	—
467	#117	C₂³×C₁₉	1	1	yes	characteristic
468	C₂×C₂²⋊C₄	—	2	4	no	—
469	#107	C₂³×C₁₉	1	2	yes	—
470	#107	C₂³×C₁₉	1	2	yes	—
471	#107	C₂³×C₁₉	1	4	yes	—
472	#106	C₂³×C₁₉	1	4	yes	—
473	#106	C₂³×C₁₉	1	2	yes	—
474	#106	C₂³×C₁₉	1	2	yes	—
475	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
476	#103	C₂³×C₁₉	1	4	yes	—
477	#103	C₂³×C₁₉	1	4	yes	—
478	#103	C₂³×C₁₉	1	4	yes	—
479	#103	C₂³×C₁₉	1	4	yes	—
480	#102	C₂³×C₁₉	1	4	yes	—
481	#102	C₂³×C₁₉	1	4	yes	—
482	#102	C₂³×C₁₉	1	4	yes	—
483	#102	C₂³×C₁₉	1	4	yes	—
484	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
485	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
486	#97	C₂³×C₁₉	1	2	yes	—
487	C₄×C₈	C₂³×C₁₉	1	2	yes	—
488	C₁₉	#62273	1	1	yes	characteristic, direct product factor, Sylow
489	C₂⁴	—	2	2	no	—
490	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
491	#41	—	4	1	no	—
492	#41	—	4	1	no	—
493	#41	—	4	4	no	—
494	#41	—	4	4	no	—
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	4	2	no	—
498	C₂×Q₈	—	4	2	no	—
499	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	2	4	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	2	no	—
506	C₂×D₄	—	4	2	no	—
507	C₂×D₄	—	4	2	no	—
508	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
509	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
510	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
511	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	4	1	no	—
516	C₂²×C₄	—	4	1	no	—
517	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
522	Q₁₆	—	4	2	no	—
523	Q₁₆	—	4	2	no	—
524	SD₁₆	—	2	8	no	—
525	SD₁₆	—	4	4	no	—
526	D₈	—	4	2	no	—
527	D₈	—	4	2	no	—
528	M₁₆	—	4	1	no	—
529	M₁₆	—	4	2	no	—
530	M₁₆	—	4	1	no	—
531	C₂×C₈	—	2	2	no	—
532	C₂×C₈	—	2	4	no	—
533	C₂×C₈	—	2	4	no	—
534	C₂×C₈	—	4	2	no	—
535	C₂×C₈	—	4	1	no	—
536	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
537	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
538	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
539	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
540	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
547	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
548	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
549	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	4	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	4	no	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
563	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
564	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	4	no	—
569	C₄²	C₂⁴×C₁₉	1	2	yes	—
570	C₂³	—	2	4	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	8	2	no	—
574	C₂³	—	8	4	no	—
575	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
576	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
577	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
578	Q₈	—	2	4	no	—
579	Q₈	—	2	4	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	8	2	no	—
582	Q₈	—	8	4	no	—
583	D₄	—	2	4	no	—
584	D₄	—	2	4	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	4	no	—
588	D₄	—	8	2	no	—
589	D₄	—	8	4	no	—
590	D₄	—	8	4	no	—
591	D₄	—	8	4	no	—
592	D₄	—	8	4	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	8	4	no	—
605	C₂×C₄	—	8	4	no	—
606	C₂×C₄	—	8	2	no	—
607	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
608	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
609	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
610	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
611	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
612	C₈	—	2	1	no	—
613	C₈	—	2	2	no	—
614	C₈	—	2	2	no	—
615	C₈	—	2	2	no	—
616	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	4	4	no	—
625	C₂²	—	4	4	no	—
626	C₂²	—	4	4	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	16	4	no	—
629	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
630	C₄	—	2	2	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	4	no	—
634	C₄	—	4	4	no	—
635	C₄	—	4	4	no	—
636	C₄	—	4	4	no	—
637	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
638	C₄	C₁₉×#585	1	1	yes	characteristic
639	C₂	—	4	1	no	—
640	C₂	—	4	2	no	—
641	C₂	—	4	2	no	—
642	C₂	—	8	4	no	—
643	C₂	C₁₉×#3496	1	1	yes	characteristic
644	C₂	C₁₉×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3540	C₂	semidirect
2. C₁₉×#3340	C₂	semidirect
3. C₁₉×#3319	C₂	semidirect
4. C₁₉×#3313	C₂	semidirect
5. C₁₉×#3282	C₂	semidirect
6. C₁₉×#3262	C₂	semidirect
7. C₁₉×#3202	C₂	semidirect
8. C₁₉×#3199	C₂	semidirect
9. C₁₉×#3197	C₂	semidirect
10. C₁₉×#3173	C₂	semidirect
11. C₁₉×#3057	C₂	semidirect
12. C₁₉×#3050	C₂	semidirect
13. C₁₉×#2929	C₂	semidirect
15. C₂²×SD₁₆×C₁₉	C₂²	semidirect
17. C₂³×C₈×C₁₉	C₂²	semidirect
21. C₁₉×#556	C₂²	semidirect
25. C₁₉×#546	C₂²	semidirect
27. C₁₉×#542	C₂²	semidirect
32. C₁₉×#525	C₂²	semidirect
33. C₁₉×#498	C₂²	semidirect
34. C₁₉×#495	C₂²	semidirect
35. C₁₉×#489	C₂²	semidirect
36. C₁₉×#485	C₂²	semidirect
37. C₁₉×#485	C₂²	semidirect
38. C₁₉×#482	C₂²	semidirect
39. C₁₉×#482	C₂²	semidirect
40. C₁₉×#477	C₂²	semidirect
41. C₁₉×#474	C₂²	semidirect
42. C₁₉×#470	C₂²	semidirect
44. C₁₉×#468	C₂²	semidirect
45. C₁₉×#468	C₂²	semidirect
46. C₁₉×#467	C₂²	semidirect
47. C₁₉×#467	C₂²	semidirect
50. C₁₉×#465	C₂²	semidirect
51. C₁₉×#465	C₂²	semidirect
52. C₁₉×#465	C₂²	semidirect
53. C₁₉×#464	C₂²	semidirect
54. C₁₉×#463	C₂²	semidirect
55. C₁₉×#452	C₂²	semidirect
56. C₁₉×#451	C₂²	semidirect
58. C₁₉×#447	C₂²	semidirect
59. C₁₉×#442	C₂²	semidirect
60. C₁₉×#441	C₂²	semidirect
61. C₄×SD₁₆×C₁₉	C₂²	semidirect
62. C₁₉×#435	C₂²	semidirect
63. C₈×D₄×C₁₉	C₂²	semidirect
64. C₁₉×#427	C₂²	semidirect
65. C₁₉×#427	C₂²	semidirect
66. C₁₉×#424	C₂²	semidirect
67. C₁₉×#419	C₂²	semidirect
68. C₁₉×#418	C₂²	semidirect
69. C₁₉×#416	C₂²	semidirect
71. C₁₉×#407	C₂²	semidirect
72. C₁₉×#405	C₂²	semidirect
247. #62273	C₁₉	direct (N × H)
295. #3540	C₂×C₁₉	semidirect
296. #3340	C₂×C₁₉	semidirect
297. #3319	C₂×C₁₉	semidirect
298. #3313	C₂×C₁₉	semidirect
299. #3282	C₂×C₁₉	semidirect
300. #3262	C₂×C₁₉	semidirect
301. #3202	C₂×C₁₉	semidirect
302. #3199	C₂×C₁₉	semidirect
303. #3197	C₂×C₁₉	semidirect
304. #3173	C₂×C₁₉	semidirect
305. #3057	C₂×C₁₉	semidirect
306. #3050	C₂×C₁₉	semidirect
307. #2929	C₂×C₁₉	semidirect
331. C₂²×SD₁₆	C₂²×C₁₉	semidirect
333. C₂³×C₈	C₂²×C₁₉	semidirect
337. #556	C₂²×C₁₉	semidirect
341. #546	C₂²×C₁₉	semidirect
343. #542	C₂²×C₁₉	semidirect
348. #525	C₂²×C₁₉	semidirect
349. #498	C₂²×C₁₉	semidirect
350. #495	C₂²×C₁₉	semidirect
351. #489	C₂²×C₁₉	semidirect
352. #485	C₂²×C₁₉	semidirect
353. #485	C₂²×C₁₉	semidirect
354. #482	C₂²×C₁₉	semidirect
355. #482	C₂²×C₁₉	semidirect
356. #477	C₂²×C₁₉	semidirect
357. #474	C₂²×C₁₉	semidirect
358. #470	C₂²×C₁₉	semidirect
360. #468	C₂²×C₁₉	semidirect
361. #468	C₂²×C₁₉	semidirect
362. #467	C₂²×C₁₉	semidirect
363. #467	C₂²×C₁₉	semidirect
366. #465	C₂²×C₁₉	semidirect
367. #465	C₂²×C₁₉	semidirect
368. #465	C₂²×C₁₉	semidirect
369. #464	C₂²×C₁₉	semidirect
370. #463	C₂²×C₁₉	semidirect
371. #452	C₂²×C₁₉	semidirect
372. #451	C₂²×C₁₉	semidirect
374. #447	C₂²×C₁₉	semidirect
375. #442	C₂²×C₁₉	semidirect
376. #441	C₂²×C₁₉	semidirect
377. C₄×SD₁₆	C₂²×C₁₉	semidirect
378. #435	C₂²×C₁₉	semidirect
379. C₈×D₄	C₂²×C₁₉	semidirect
380. #427	C₂²×C₁₉	semidirect
381. #427	C₂²×C₁₉	semidirect
382. #424	C₂²×C₁₉	semidirect
383. #419	C₂²×C₁₉	semidirect
384. #418	C₂²×C₁₉	semidirect
385. #416	C₂²×C₁₉	semidirect
387. #407	C₂²×C₁₉	semidirect
388. #405	C₂²×C₁₉	semidirect
488. C₁₉	#62273	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×#3540	2
C₁₉×#3340	2
C₁₉×#3319	2
C₁₉×#3313	2
C₁₉×#3282	2
C₁₉×#3262	2
C₁₉×#3202	2
C₁₉×#3199	2
C₁₉×#3197	2
C₁₉×#3173	2
C₁₉×#3057	2
C₁₉×#3050	2
C₁₉×#2929	2
#62273	19

Subgroups — C19×#62273 #18068232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62273 #18068232