Subgroups — C₁₉×#24523 #18030482

Order 4864.

874 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3094	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#448	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2064	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×#1930	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1900	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1855	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1784	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×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×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#482	—	2	1	no	—
18	C₁₉×#482	—	2	1	no	—
19	C₁₉×#481	—	2	1	no	—
20	C₁₉×#480	—	2	1	no	—
21	C₁₉×#448	—	2	1	no	—
22	C₁₉×#448	—	2	1	no	—
23	C₁₉×#448	—	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	—
28	C₁₉×#428	C₂²	1	1	yes	characteristic
29	C₁₉×#428	C₂²	1	1	yes	characteristic
30	C₁₉×#424	C₂²	1	2	yes	—
31	C₁₉×#419	—	2	1	no	—
32	C₁₉×#419	—	2	1	no	—
33	C₁₉×#419	C₂²	1	2	yes	—
34	C₁₉×#419	C₂²	1	2	yes	—
35	C₁₉×#418	C₂²	1	1	yes	characteristic
36	C₁₉×#418	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#103	—	2	1	no	—
38	C₂×C₁₉×#103	—	2	1	no	—
39	C₂×C₁₉×#103	C₂²	1	2	yes	—
40	C₂×C₁₉×#101	C₂²	1	2	yes	—
41	C₂×C₁₉×#101	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	—
47	C₁₉×#343	C₂²	1	2	yes	—
48	C₁₉×#341	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	—	2	4	no	—
51	C₂²×Q₈×C₁₉	—	2	1	no	—
52	C₂²×Q₈×C₁₉	—	2	1	no	—
53	C₂²×Q₈×C₁₉	—	2	1	no	—
54	C₂²×Q₈×C₁₉	—	2	1	no	—
55	C₂²×Q₈×C₁₉	—	4	2	no	—
56	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₉	—	2	1	no	—
58	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	—	2	1	no	—
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×SD₁₆×C₁₉	—	2	4	no	—
62	C₂×SD₁₆×C₁₉	—	2	2	no	—
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×SD₁₆×C₁₉	—	4	2	no	—
65	C₂×M₁₆×C₁₉	—	2	1	no	—
66	C₂×M₁₆×C₁₉	—	4	2	no	—
67	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
69	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
70	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
73	C₁₉×#121	—	2	1	no	—
74	C₁₉×#121	—	2	1	no	—
75	C₁₉×#121	—	2	1	no	—
76	C₁₉×#121	—	2	1	no	—
77	C₁₉×#117	—	2	1	no	—
78	C₁₉×#117	—	2	1	no	—
79	C₁₉×#117	D₄	1	1	yes	characteristic
80	C₁₉×#117	D₄	1	1	yes	characteristic
81	C₁₉×#117	C₂³	1	1	yes	characteristic
82	C₁₉×#117	C₂³	1	1	yes	characteristic
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	2	no	—
97	C₁₉×#103	—	2	2	no	—
98	C₁₉×#103	—	2	2	no	—
99	C₁₉×#103	—	2	2	no	—
100	C₁₉×#103	—	2	2	no	—
101	C₁₉×#103	—	2	2	no	—
102	C₁₉×#102	—	2	1	no	—
103	C₁₉×#102	—	2	1	no	—
104	C₁₉×#102	—	2	1	no	—
105	C₁₉×#102	—	2	1	no	—
106	C₁₉×#101	—	2	4	no	—
107	C₁₉×#101	—	4	2	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	1	no	—
119	C₂⁴×C₁₉	#41	1	1	yes	characteristic
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	2	4	no	—
122	C₂×Q₈×C₁₉	—	2	4	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	2	no	—
125	C₂×Q₈×C₁₉	—	2	2	no	—
126	C₂×Q₈×C₁₉	—	2	2	no	—
127	C₂×Q₈×C₁₉	—	4	4	no	—
128	C₂×Q₈×C₁₉	—	4	4	no	—
129	C₂×Q₈×C₁₉	—	4	4	no	—
130	C₂×Q₈×C₁₉	—	4	2	no	—
131	C₂×Q₈×C₁₉	—	4	2	no	—
132	C₂×Q₈×C₁₉	—	4	1	no	—
133	C₂×Q₈×C₁₉	—	4	1	no	—
134	C₂×Q₈×C₁₉	#41	1	4	yes	—
135	C₂×D₄×C₁₉	—	2	1	no	—
136	C₂×D₄×C₁₉	—	2	1	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	4	1	no	—
140	C₂×D₄×C₁₉	—	4	1	no	—
141	C₂×D₄×C₁₉	—	8	2	no	—
142	C₂²×C₄×C₁₉	—	2	2	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	2	1	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	—	4	4	no	—
149	C₂²×C₄×C₁₉	—	4	1	no	—
150	C₂²×C₄×C₁₉	—	4	1	no	—
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	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
157	SD₁₆×C₁₉	—	4	4	no	—
158	SD₁₆×C₁₉	—	4	4	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	—	2	2	no	—
165	M₁₆×C₁₉	—	4	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	2	no	—
170	C₂×C₈×C₁₉	—	2	1	no	—
171	C₂×C₈×C₁₉	—	2	1	no	—
172	C₂×C₈×C₁₉	—	4	2	no	—
173	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
179	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₁₉	—	2	1	no	—
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	—	4	1	no	—
188	C₂²⋊C₄×C₁₉	—	4	1	no	—
189	C₄²×C₁₉	—	2	1	no	—
190	C₄²×C₁₉	—	2	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	#24523	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂³×C₁₉	—	2	2	no	—
195	C₂³×C₁₉	—	2	2	no	—
196	C₂³×C₁₉	—	4	1	no	—
197	C₂³×C₁₉	—	4	1	no	—
198	C₂³×C₁₉	—	4	2	no	—
199	C₂³×C₁₉	—	8	1	no	—
200	C₂³×C₁₉	—	8	1	no	—
201	C₂³×C₁₉	#121	1	1	yes	characteristic
202	C₂³×C₁₉	#121	1	1	yes	characteristic
203	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
204	Q₈×C₁₉	—	2	4	no	—
205	Q₈×C₁₉	—	2	4	no	—
206	Q₈×C₁₉	—	4	4	no	—
207	Q₈×C₁₉	—	4	4	no	—
208	Q₈×C₁₉	—	4	2	no	—
209	Q₈×C₁₉	—	4	2	no	—
210	D₄×C₁₉	—	4	1	no	—
211	D₄×C₁₉	—	4	1	no	—
212	D₄×C₁₉	—	4	2	no	—
213	D₄×C₁₉	—	8	2	no	—
214	D₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	1	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	2	1	no	—
219	C₂×C₄×C₁₉	—	2	1	no	—
220	C₂×C₄×C₁₉	—	2	2	no	—
221	C₂×C₄×C₁₉	—	2	2	no	—
222	C₂×C₄×C₁₉	—	2	1	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	4	no	—
227	C₂×C₄×C₁₉	—	4	4	no	—
228	C₂×C₄×C₁₉	—	4	4	no	—
229	C₂×C₄×C₁₉	—	4	2	no	—
230	C₂×C₄×C₁₉	—	4	2	no	—
231	C₂×C₄×C₁₉	—	4	2	no	—
232	C₂×C₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	8	1	no	—
234	C₂×C₄×C₁₉	—	8	1	no	—
235	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
236	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
237	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
240	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
241	C₈×C₁₉	—	2	2	no	—
242	C₈×C₁₉	—	2	2	no	—
243	C₈×C₁₉	—	4	1	no	—
244	C₈×C₁₉	—	4	2	no	—
245	C₈×C₁₉	—	4	1	no	—
246	C₈×C₁₉	—	4	2	no	—
247	#3094	C₂×C₁₉	1	1	yes	characteristic
248	C₂×#448	C₂×C₁₉	1	1	yes	characteristic
249	#2924	C₂×C₁₉	1	1	yes	characteristic, complemented
250	C₂×#419	C₂×C₁₉	1	1	yes	characteristic, complemented
251	#2064	C₂×C₁₉	1	2	yes	complemented
252	#2046	C₂×C₁₉	1	2	yes	complemented
253	#1977	C₂×C₁₉	1	2	yes	complemented
254	#1930	C₂×C₁₉	1	2	yes	complemented
255	#1900	C₂×C₁₉	1	1	yes	characteristic
256	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
257	#1784	C₂×C₁₉	1	1	yes	characteristic, complemented
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	—	2	1	no	—
264	C₂²×C₁₉	—	2	1	no	—
265	C₂²×C₁₉	—	4	4	no	—
266	C₂²×C₁₉	—	8	1	no	—
267	C₂²×C₁₉	—	8	1	no	—
268	C₂²×C₁₉	—	8	1	no	—
269	C₂²×C₁₉	—	16	2	no	—
270	C₂²×C₁₉	#471	1	2	yes	—
271	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
272	C₂²×C₁₉	#551	1	2	yes	—
273	C₄×C₁₉	—	2	1	no	—
274	C₄×C₁₉	—	2	1	no	—
275	C₄×C₁₉	—	4	4	no	—
276	C₄×C₁₉	—	4	1	no	—
277	C₄×C₁₉	—	4	1	no	—
278	C₄×C₁₉	—	4	1	no	—
279	C₄×C₁₉	—	4	1	no	—
280	C₄×C₁₉	—	8	1	no	—
281	C₄×C₁₉	#525	1	1	yes	characteristic
282	C₄×C₁₉	#535	1	1	yes	characteristic
283	C₄×C₁₉	#546	1	2	yes	—
284	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
285	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
286	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
287	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
289	#482	—	2	1	no	—
290	#482	—	2	1	no	—
291	#481	—	2	1	no	—
292	#480	—	2	1	no	—
293	#448	—	2	1	no	—
294	#448	—	2	1	no	—
295	#448	—	2	2	no	—
296	#433	—	2	2	no	—
297	#432	—	2	1	no	—
298	#431	—	2	1	no	—
299	C₂×#108	C₂²×C₁₉	1	2	yes	—
300	#428	C₂²×C₁₉	1	1	yes	characteristic
301	#428	C₂²×C₁₉	1	1	yes	characteristic
302	#424	C₂²×C₁₉	1	2	yes	—
303	#419	—	2	1	no	—
304	#419	—	2	1	no	—
305	#419	C₂²×C₁₉	1	2	yes	—
306	#419	C₂²×C₁₉	1	2	yes	—
307	#418	C₂²×C₁₉	1	1	yes	characteristic
308	#418	C₂²×C₁₉	1	1	yes	characteristic
309	C₂×#103	—	2	1	no	—
310	C₂×#103	—	2	1	no	—
311	C₂×#103	C₂²×C₁₉	1	2	yes	—
312	C₂×#101	C₂²×C₁₉	1	2	yes	—
313	C₂×#101	C₂²×C₁₉	1	2	yes	—
314	C₂×#100	C₂²×C₁₉	1	2	yes	—
315	#407	C₂²×C₁₉	1	1	yes	characteristic
316	#407	C₂²×C₁₉	1	1	yes	characteristic
317	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
318	#405	C₂²×C₁₉	1	2	yes	—
319	#343	C₂²×C₁₉	1	2	yes	—
320	#341	C₂²×C₁₉	1	2	yes	—
321	C₂×C₁₉	—	2	2	no	—
322	C₂×C₁₉	—	2	2	no	—
323	C₂×C₁₉	—	4	1	no	—
324	C₂×C₁₉	—	16	1	no	—
325	C₂×C₁₉	#2411	1	1	yes	characteristic
326	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
327	C₂×C₁₉	#3069	1	1	yes	characteristic
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×Q₈	—	2	4	no	—
330	C₂²×Q₈	—	2	1	no	—
331	C₂²×Q₈	—	2	1	no	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×Q₈	—	4	2	no	—
335	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
336	C₂²×D₄	—	2	1	no	—
337	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
340	C₂×SD₁₆	—	2	4	no	—
341	C₂×SD₁₆	—	2	2	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	4	2	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	4	2	no	—
346	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
347	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
348	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
349	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	#121	—	2	1	no	—
355	#121	—	2	1	no	—
356	#117	—	2	1	no	—
357	#117	—	2	1	no	—
358	#117	D₄×C₁₉	1	1	yes	characteristic
359	#117	D₄×C₁₉	1	1	yes	characteristic
360	#117	C₂³×C₁₉	1	1	yes	characteristic
361	#117	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
363	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	#108	—	4	2	no	—
369	#107	—	2	1	no	—
370	#107	—	2	1	no	—
371	#106	—	2	1	no	—
372	#106	—	2	1	no	—
373	C₄⋊C₈	—	2	2	no	—
374	C₄⋊C₈	—	2	2	no	—
375	#103	—	2	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#103	—	2	2	no	—
379	#103	—	2	2	no	—
380	#103	—	2	2	no	—
381	#102	—	2	1	no	—
382	#102	—	2	1	no	—
383	#102	—	2	1	no	—
384	#102	—	2	1	no	—
385	#101	—	2	4	no	—
386	#101	—	4	2	no	—
387	#100	—	4	2	no	—
388	C₂²⋊C₈	—	2	1	no	—
389	C₂²⋊C₈	—	2	1	no	—
390	C₂²⋊C₈	—	2	1	no	—
391	C₂²⋊C₈	—	2	1	no	—
392	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
393	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
394	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
395	#97	—	2	2	no	—
396	C₄×C₈	—	2	2	no	—
397	C₁₉	#24523	1	1	yes	characteristic, direct product factor, Sylow
398	C₂⁴	—	2	1	no	—
399	C₂⁴	#41×C₁₉	1	1	yes	characteristic
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	4	no	—
409	C₂×Q₈	—	4	4	no	—
410	C₂×Q₈	—	4	2	no	—
411	C₂×Q₈	—	4	2	no	—
412	C₂×Q₈	—	4	1	no	—
413	C₂×Q₈	—	4	1	no	—
414	C₂×Q₈	#41×C₁₉	1	4	yes	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	8	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
435	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
437	SD₁₆	—	4	4	no	—
438	SD₁₆	—	4	4	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	2	2	no	—
445	M₁₆	—	4	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	4	2	no	—
453	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
454	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
460	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
461	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
462	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
463	C₂²⋊C₄	—	2	1	no	—
464	C₂²⋊C₄	—	2	1	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	8	1	no	—
479	C₂³	—	8	1	no	—
480	C₂³	C₁₉×#121	1	1	yes	characteristic
481	C₂³	C₁₉×#121	1	1	yes	characteristic
482	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
483	Q₈	—	2	4	no	—
484	Q₈	—	2	4	no	—
485	Q₈	—	4	4	no	—
486	Q₈	—	4	4	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	2	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	2	no	—
492	D₄	—	8	2	no	—
493	D₄	—	8	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	8	1	no	—
513	C₂×C₄	—	8	1	no	—
514	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
515	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
518	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
519	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	2	no	—
524	C₈	—	4	1	no	—
525	C₈	—	4	2	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	4	4	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	16	2	no	—
538	C₂²	C₁₉×#471	1	2	yes	—
539	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
540	C₂²	C₁₉×#551	1	2	yes	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₄	—	8	1	no	—
549	C₄	C₁₉×#525	1	1	yes	characteristic
550	C₄	C₁₉×#535	1	1	yes	characteristic
551	C₄	C₁₉×#546	1	2	yes	—
552	C₂	—	2	2	no	—
553	C₂	—	2	2	no	—
554	C₂	—	4	1	no	—
555	C₂	—	16	1	no	—
556	C₂	C₁₉×#2411	1	1	yes	characteristic
557	C₂	C₂×C₁₉×#471	1	1	yes	characteristic
558	C₂	C₁₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#121	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
3. C₁₉×#2924	C₂	semidirect
4. C₂×C₁₉×#419	C₂	semidirect
5. C₁₉×#2064	C₂	semidirect
6. C₁₉×#2046	C₂	semidirect
7. C₁₉×#1977	C₂	semidirect
8. C₁₉×#1930	C₂	semidirect
10. C₁₉×#1855	C₂	semidirect
11. C₁₉×#1784	C₂	semidirect
193. #24523	C₁₉	direct (N × H)
249. #2924	C₂×C₁₉	semidirect
250. C₂×#419	C₂×C₁₉	semidirect
251. #2064	C₂×C₁₉	semidirect
252. #2046	C₂×C₁₉	semidirect
253. #1977	C₂×C₁₉	semidirect
254. #1930	C₂×C₁₉	semidirect
256. #1855	C₂×C₁₉	semidirect
257. #1784	C₂×C₁₉	semidirect
397. C₁₉	#24523	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×#3094	2
C₂×C₁₉×#448	2
C₁₉×#2924	2
C₂×C₁₉×#419	2
C₁₉×#2064	2
C₁₉×#2046	2
C₁₉×#1977	2
C₁₉×#1930	2
C₁₉×#1900	2
C₁₉×#1855	2
C₁₉×#1784	2
#24523	19

Subgroups — C19×#24523 #18030482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24523 #18030482