Subgroups — C₁₉×#24521 #18030480

Order 4864.

976 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3095	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#450	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#418	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2063	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2046	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1977	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1931	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1783	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#485	—	2	1	no	—
18	C₁₉×#485	—	2	1	no	—
19	C₁₉×#484	—	2	1	no	—
20	C₁₉×#483	—	2	1	no	—
21	C₁₉×#450	—	2	1	no	—
22	C₁₉×#450	—	2	1	no	—
23	C₁₉×#450	—	2	2	no	—
24	C₁₉×#433	—	2	2	no	—
25	C₁₉×#432	—	2	1	no	—
26	C₁₉×#431	—	2	1	no	—
27	C₂×C₁₉×#108	C₂²	1	2	yes	complemented
28	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#428	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#424	C₂²	1	2	yes	complemented
31	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#419	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#418	—	2	1	no	—
34	C₁₉×#418	—	2	1	no	—
35	C₁₉×#418	C₂²	1	2	yes	—
36	C₁₉×#418	C₂²	1	2	yes	—
37	C₂×C₁₉×#102	—	2	1	no	—
38	C₂×C₁₉×#102	—	2	1	no	—
39	C₂×C₁₉×#102	C₂²	1	2	yes	—
40	C₂×C₁₉×#101	C₂²	1	2	yes	complemented
41	C₂×C₁₉×#100	C₂²	1	2	yes	—
42	C₂×C₁₉×#100	C₂²	1	2	yes	—
43	C₁₉×#407	C₂²	1	1	yes	characteristic
44	C₁₉×#407	C₂²	1	1	yes	characteristic
45	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₉×#405	C₂²	1	2	yes	complemented
47	C₁₉×#343	C₂²	1	2	yes	complemented
48	C₁₉×#341	C₂²	1	2	yes	complemented
49	C₂⁵×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	—	2	4	no	—
52	C₂²×D₄×C₁₉	—	2	1	no	—
53	C₂²×D₄×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	—	2	1	no	—
55	C₂²×D₄×C₁₉	—	2	1	no	—
56	C₂²×D₄×C₁₉	—	2	1	no	—
57	C₂²×D₄×C₁₉	—	4	2	no	—
58	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂×SD₁₆×C₁₉	—	2	4	no	—
61	C₂×SD₁₆×C₁₉	—	2	2	no	—
62	C₂×SD₁₆×C₁₉	—	2	2	no	—
63	C₂×SD₁₆×C₁₉	—	4	2	no	—
64	C₂×M₁₆×C₁₉	—	2	1	no	—
65	C₂×M₁₆×C₁₉	—	4	2	no	—
66	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
68	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
69	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₉	—	2	1	no	—
71	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
72	C₁₉×C₂²⋊Q₈	—	2	1	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×#117	—	2	1	no	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	D₄	1	1	yes	characteristic
79	C₁₉×#117	D₄	1	1	yes	characteristic
80	C₁₉×#117	C₂³	1	1	yes	characteristic
81	C₁₉×#117	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₁₉×#108	—	4	2	no	—
90	C₁₉×#107	—	2	1	no	—
91	C₁₉×#107	—	2	1	no	—
92	C₁₉×#106	—	2	1	no	—
93	C₁₉×#106	—	2	1	no	—
94	C₁₉×C₄⋊C₈	—	2	2	no	—
95	C₁₉×C₄⋊C₈	—	2	2	no	—
96	C₁₉×#103	—	2	1	no	—
97	C₁₉×#103	—	2	1	no	—
98	C₁₉×#103	—	2	1	no	—
99	C₁₉×#103	—	2	1	no	—
100	C₁₉×#102	—	2	2	no	—
101	C₁₉×#102	—	2	2	no	—
102	C₁₉×#102	—	2	2	no	—
103	C₁₉×#102	—	2	2	no	—
104	C₁₉×#102	—	2	2	no	—
105	C₁₉×#102	—	2	2	no	—
106	C₁₉×#101	—	4	2	no	—
107	C₁₉×#100	—	2	4	no	—
108	C₁₉×#100	—	4	2	no	—
109	C₁₉×C₂²⋊C₈	—	2	1	no	—
110	C₁₉×C₂²⋊C₈	—	2	1	no	—
111	C₁₉×C₂²⋊C₈	—	2	1	no	—
112	C₁₉×C₂²⋊C₈	—	2	1	no	—
113	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
114	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
115	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
116	C₁₉×#97	—	2	2	no	—
117	C₄×C₈×C₁₉	—	2	2	no	—
118	C₂⁴×C₁₉	—	2	2	no	—
119	C₂⁴×C₁₉	—	4	4	no	—
120	C₂⁴×C₁₉	—	4	1	no	—
121	C₂⁴×C₁₉	—	4	1	no	—
122	C₂⁴×C₁₉	—	8	2	no	—
123	C₂⁴×C₁₉	—	8	2	no	—
124	C₂⁴×C₁₉	#41	1	1	yes	characteristic
125	C₂×Q₈×C₁₉	—	2	1	no	—
126	C₂×Q₈×C₁₉	—	2	1	no	—
127	C₂×Q₈×C₁₉	—	2	2	no	—
128	C₂×Q₈×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	2	no	—
132	C₂×D₄×C₁₉	—	2	2	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	—	4	4	no	—
137	C₂×D₄×C₁₉	—	4	4	no	—
138	C₂×D₄×C₁₉	—	4	4	no	—
139	C₂×D₄×C₁₉	—	4	2	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	4	1	no	—
142	C₂×D₄×C₁₉	—	4	1	no	—
143	C₂×D₄×C₁₉	#41	1	4	yes	—
144	C₂²×C₄×C₁₉	—	2	2	no	—
145	C₂²×C₄×C₁₉	—	2	2	no	—
146	C₂²×C₄×C₁₉	—	2	1	no	—
147	C₂²×C₄×C₁₉	—	2	1	no	—
148	C₂²×C₄×C₁₉	—	2	1	no	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
156	SD₁₆×C₁₉	—	4	4	no	—
157	SD₁₆×C₁₉	—	4	4	no	—
158	M₁₆×C₁₉	—	2	2	no	—
159	M₁₆×C₁₉	—	2	2	no	—
160	M₁₆×C₁₉	—	2	2	no	—
161	M₁₆×C₁₉	—	2	2	no	—
162	M₁₆×C₁₉	—	2	2	no	—
163	M₁₆×C₁₉	—	2	2	no	—
164	M₁₆×C₁₉	—	4	2	no	—
165	C₂×C₈×C₁₉	—	2	2	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	2	1	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	4	2	no	—
172	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	4	1	no	—
179	C₄⋊C₄×C₁₉	—	4	1	no	—
180	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
182	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
183	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₂²⋊C₄×C₁₉	—	2	1	no	—
185	C₂²⋊C₄×C₁₉	—	2	1	no	—
186	C₂²⋊C₄×C₁₉	—	2	1	no	—
187	C₂²⋊C₄×C₁₉	—	2	1	no	—
188	C₂²⋊C₄×C₁₉	—	4	1	no	—
189	C₂²⋊C₄×C₁₉	—	4	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	#24521	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	2	4	no	—
198	C₂³×C₁₉	—	4	1	no	—
199	C₂³×C₁₉	—	4	4	no	—
200	C₂³×C₁₉	—	4	4	no	—
201	C₂³×C₁₉	—	4	2	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	8	2	no	—
204	C₂³×C₁₉	—	8	2	no	—
205	C₂³×C₁₉	—	8	2	no	—
206	C₂³×C₁₉	—	8	2	no	—
207	C₂³×C₁₉	—	8	2	no	—
208	C₂³×C₁₉	—	8	16	no	—
209	C₂³×C₁₉	—	8	2	no	—
210	C₂³×C₁₉	#121	1	1	yes	characteristic
211	C₂³×C₁₉	#121	1	1	yes	characteristic
212	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
213	Q₈×C₁₉	—	4	1	no	—
214	Q₈×C₁₉	—	4	1	no	—
215	Q₈×C₁₉	—	4	2	no	—
216	D₄×C₁₉	—	2	4	no	—
217	D₄×C₁₉	—	2	4	no	—
218	D₄×C₁₉	—	4	4	no	—
219	D₄×C₁₉	—	4	4	no	—
220	D₄×C₁₉	—	4	2	no	—
221	D₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	2	2	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	1	no	—
227	C₂×C₄×C₁₉	—	2	2	no	—
228	C₂×C₄×C₁₉	—	2	2	no	—
229	C₂×C₄×C₁₉	—	2	1	no	—
230	C₂×C₄×C₁₉	—	2	1	no	—
231	C₂×C₄×C₁₉	—	2	1	no	—
232	C₂×C₄×C₁₉	—	2	1	no	—
233	C₂×C₄×C₁₉	—	4	2	no	—
234	C₂×C₄×C₁₉	—	4	1	no	—
235	C₂×C₄×C₁₉	—	4	1	no	—
236	C₂×C₄×C₁₉	—	4	2	no	—
237	C₂×C₄×C₁₉	—	8	1	no	—
238	C₂×C₄×C₁₉	—	8	1	no	—
239	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
240	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
241	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
245	C₈×C₁₉	—	2	2	no	—
246	C₈×C₁₉	—	2	2	no	—
247	C₈×C₁₉	—	4	1	no	—
248	C₈×C₁₉	—	4	2	no	—
249	C₈×C₁₉	—	4	1	no	—
250	C₈×C₁₉	—	4	2	no	—
251	#3095	C₂×C₁₉	1	1	yes	characteristic, complemented
252	C₂×#450	C₂×C₁₉	1	1	yes	characteristic
253	#2924	C₂×C₁₉	1	1	yes	characteristic, complemented
254	C₂×#418	C₂×C₁₉	1	1	yes	characteristic
255	#2063	C₂×C₁₉	1	2	yes	complemented
256	#2046	C₂×C₁₉	1	2	yes	complemented
257	#1977	C₂×C₁₉	1	2	yes	complemented
258	#1931	C₂×C₁₉	1	2	yes	complemented
259	#1901	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
261	#1783	C₂×C₁₉	1	1	yes	characteristic
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	2	1	no	—
266	C₂²×C₁₉	—	2	1	no	—
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	4	4	no	—
270	C₂²×C₁₉	—	4	4	no	—
271	C₂²×C₁₉	—	8	4	no	—
272	C₂²×C₁₉	—	8	4	no	—
273	C₂²×C₁₉	—	8	8	no	—
274	C₂²×C₁₉	—	8	8	no	—
275	C₂²×C₁₉	—	8	2	no	—
276	C₂²×C₁₉	—	8	2	no	—
277	C₂²×C₁₉	#471	1	2	yes	—
278	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
279	C₂²×C₁₉	#551	1	2	yes	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	4	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	1	no	—
285	C₄×C₁₉	—	4	1	no	—
286	C₄×C₁₉	—	8	1	no	—
287	C₄×C₁₉	—	8	1	no	—
288	C₄×C₁₉	#525	1	1	yes	characteristic
289	C₄×C₁₉	#535	1	1	yes	characteristic
290	C₄×C₁₉	#546	1	2	yes	—
291	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
292	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
293	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
295	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
296	#485	—	2	1	no	—
297	#485	—	2	1	no	—
298	#484	—	2	1	no	—
299	#483	—	2	1	no	—
300	#450	—	2	1	no	—
301	#450	—	2	1	no	—
302	#450	—	2	2	no	—
303	#433	—	2	2	no	—
304	#432	—	2	1	no	—
305	#431	—	2	1	no	—
306	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
307	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
308	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
309	#424	C₂²×C₁₉	1	2	yes	complemented
310	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
311	#419	C₂²×C₁₉	1	1	yes	characteristic, complemented
312	#418	—	2	1	no	—
313	#418	—	2	1	no	—
314	#418	C₂²×C₁₉	1	2	yes	—
315	#418	C₂²×C₁₉	1	2	yes	—
316	C₂×#102	—	2	1	no	—
317	C₂×#102	—	2	1	no	—
318	C₂×#102	C₂²×C₁₉	1	2	yes	—
319	C₂×#101	C₂²×C₁₉	1	2	yes	complemented
320	C₂×#100	C₂²×C₁₉	1	2	yes	—
321	C₂×#100	C₂²×C₁₉	1	2	yes	—
322	#407	C₂²×C₁₉	1	1	yes	characteristic
323	#407	C₂²×C₁₉	1	1	yes	characteristic
324	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
325	#405	C₂²×C₁₉	1	2	yes	complemented
326	#343	C₂²×C₁₉	1	2	yes	complemented
327	#341	C₂²×C₁₉	1	2	yes	complemented
328	C₂×C₁₉	—	2	2	no	—
329	C₂×C₁₉	—	2	2	no	—
330	C₂×C₁₉	—	4	1	no	—
331	C₂×C₁₉	—	8	4	no	—
332	C₂×C₁₉	#2411	1	1	yes	characteristic
333	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
334	C₂×C₁₉	#3068	1	1	yes	characteristic
335	C₂⁵	—	2	1	no	—
336	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₂²×D₄	—	2	4	no	—
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	4	2	no	—
344	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
345	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
346	C₂×SD₁₆	—	2	4	no	—
347	C₂×SD₁₆	—	2	2	no	—
348	C₂×SD₁₆	—	2	2	no	—
349	C₂×SD₁₆	—	4	2	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	4	2	no	—
352	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
353	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
354	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
355	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	#117	—	2	1	no	—
363	#117	—	2	1	no	—
364	#117	D₄×C₁₉	1	1	yes	characteristic
365	#117	D₄×C₁₉	1	1	yes	characteristic
366	#117	C₂³×C₁₉	1	1	yes	characteristic
367	#117	C₂³×C₁₉	1	1	yes	characteristic
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
370	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	#108	—	4	2	no	—
376	#107	—	2	1	no	—
377	#107	—	2	1	no	—
378	#106	—	2	1	no	—
379	#106	—	2	1	no	—
380	C₄⋊C₈	—	2	2	no	—
381	C₄⋊C₈	—	2	2	no	—
382	#103	—	2	1	no	—
383	#103	—	2	1	no	—
384	#103	—	2	1	no	—
385	#103	—	2	1	no	—
386	#102	—	2	2	no	—
387	#102	—	2	2	no	—
388	#102	—	2	2	no	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	2	2	no	—
392	#101	—	4	2	no	—
393	#100	—	2	4	no	—
394	#100	—	4	2	no	—
395	C₂²⋊C₈	—	2	1	no	—
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
400	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
401	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
402	#97	—	2	2	no	—
403	C₄×C₈	—	2	2	no	—
404	C₁₉	#24521	1	1	yes	characteristic, direct product factor, Sylow
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	4	4	no	—
407	C₂⁴	—	4	1	no	—
408	C₂⁴	—	4	1	no	—
409	C₂⁴	—	8	2	no	—
410	C₂⁴	—	8	2	no	—
411	C₂⁴	#41×C₁₉	1	1	yes	characteristic
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	2	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	—	4	4	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	—	4	2	no	—
427	C₂×D₄	—	4	2	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	#41×C₁₉	1	4	yes	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
441	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
442	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
443	SD₁₆	—	4	4	no	—
444	SD₁₆	—	4	4	no	—
445	M₁₆	—	2	2	no	—
446	M₁₆	—	2	2	no	—
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	4	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	4	2	no	—
459	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
460	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
468	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
469	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	4	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	8	2	no	—
490	C₂³	—	8	2	no	—
491	C₂³	—	8	2	no	—
492	C₂³	—	8	2	no	—
493	C₂³	—	8	2	no	—
494	C₂³	—	8	16	no	—
495	C₂³	—	8	2	no	—
496	C₂³	C₁₉×#121	1	1	yes	characteristic
497	C₂³	C₁₉×#121	1	1	yes	characteristic
498	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	2	no	—
502	D₄	—	2	4	no	—
503	D₄	—	2	4	no	—
504	D₄	—	4	4	no	—
505	D₄	—	4	4	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	8	1	no	—
524	C₂×C₄	—	8	1	no	—
525	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
526	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
529	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
530	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
531	C₈	—	2	2	no	—
532	C₈	—	2	2	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	2	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	8	4	no	—
547	C₂²	—	8	8	no	—
548	C₂²	—	8	4	no	—
549	C₂²	—	8	8	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	C₁₉×#471	1	2	yes	—
553	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
554	C₂²	C₁₉×#551	1	2	yes	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	C₁₉×#525	1	1	yes	characteristic
564	C₄	C₁₉×#535	1	1	yes	characteristic
565	C₄	C₁₉×#546	1	2	yes	—
566	C₂	—	2	2	no	—
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	8	4	no	—
570	C₂	C₁₉×#2411	1	1	yes	characteristic
571	C₂	C₂×C₁₉×#471	1	1	yes	characteristic
572	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3095	C₂	semidirect
3. C₁₉×#2924	C₂	semidirect
5. C₁₉×#2063	C₂	semidirect
6. C₁₉×#2046	C₂	semidirect
7. C₁₉×#1977	C₂	semidirect
8. C₁₉×#1931	C₂	semidirect
9. C₁₉×#1901	C₂	semidirect
10. C₁₉×#1855	C₂	semidirect
27. C₂×C₁₉×#108	C₂²	semidirect
28. C₁₉×#428	C₂²	semidirect
29. C₁₉×#428	C₂²	semidirect
30. C₁₉×#424	C₂²	semidirect
31. C₁₉×#419	C₂²	semidirect
32. C₁₉×#419	C₂²	semidirect
40. C₂×C₁₉×#101	C₂²	semidirect
46. C₁₉×#405	C₂²	semidirect
47. C₁₉×#343	C₂²	semidirect
48. C₁₉×#341	C₂²	semidirect
194. #24521	C₁₉	direct (N × H)
251. #3095	C₂×C₁₉	semidirect
253. #2924	C₂×C₁₉	semidirect
255. #2063	C₂×C₁₉	semidirect
256. #2046	C₂×C₁₉	semidirect
257. #1977	C₂×C₁₉	semidirect
258. #1931	C₂×C₁₉	semidirect
259. #1901	C₂×C₁₉	semidirect
260. #1855	C₂×C₁₉	semidirect
306. C₂×#108	C₂²×C₁₉	semidirect
307. #428	C₂²×C₁₉	semidirect
308. #428	C₂²×C₁₉	semidirect
309. #424	C₂²×C₁₉	semidirect
310. #419	C₂²×C₁₉	semidirect
311. #419	C₂²×C₁₉	semidirect
319. C₂×#101	C₂²×C₁₉	semidirect
325. #405	C₂²×C₁₉	semidirect
326. #343	C₂²×C₁₉	semidirect
327. #341	C₂²×C₁₉	semidirect
404. C₁₉	#24521	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×#3095	2
C₂×C₁₉×#450	2
C₁₉×#2924	2
C₂×C₁₉×#418	2
C₁₉×#2063	2
C₁₉×#2046	2
C₁₉×#1977	2
C₁₉×#1931	2
C₁₉×#1901	2
C₁₉×#1855	2
C₁₉×#1783	2
#24521	19

Subgroups — C19×#24521 #18030480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24521 #18030480