Subgroups — C₁₉×#24520 #18030479

Order 4864.

1002 conjugacy classes of subgroups.

The subgroup lattice has 592 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, complemented
2	C₂×C₁₉×#447	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, complemented
5	C₁₉×#2063	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2045	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1978	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1931	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1900	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, complemented
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×D₈×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×#447	—	2	1	no	—
22	C₁₉×#447	—	2	1	no	—
23	C₁₉×#447	—	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×#418	—	2	1	no	—
32	C₁₉×#418	—	2	1	no	—
33	C₁₉×#418	C₂²	1	2	yes	—
34	C₁₉×#418	C₂²	1	2	yes	—
35	C₁₉×#418	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#418	C₂²	1	1	yes	characteristic, complemented
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×#100	C₂²	1	2	yes	—
41	C₂×C₁₉×#100	C₂²	1	2	yes	—
42	C₂×C₁₉×#100	C₂²	1	2	yes	complemented
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×D₄×C₁₉	—	2	4	no	—
51	C₂²×D₄×C₁₉	—	2	1	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	1	yes	characteristic
59	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×D₈×C₁₉	—	2	4	no	—
62	C₂×D₈×C₁₉	—	2	2	no	—
63	C₂×D₈×C₁₉	—	2	2	no	—
64	C₂×D₈×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×#102	—	2	2	no	—
97	C₁₉×#102	—	2	2	no	—
98	C₁₉×#102	—	2	2	no	—
99	C₁₉×#102	—	2	2	no	—
100	C₁₉×#102	—	2	2	no	—
101	C₁₉×#102	—	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×#100	—	2	4	no	—
107	C₁₉×#100	—	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	2	no	—
119	C₂⁴×C₁₉	—	2	1	no	—
120	C₂⁴×C₁₉	—	4	4	no	—
121	C₂⁴×C₁₉	—	4	1	no	—
122	C₂⁴×C₁₉	—	4	1	no	—
123	C₂⁴×C₁₉	—	8	2	no	—
124	C₂⁴×C₁₉	—	8	2	no	—
125	C₂⁴×C₁₉	#41	1	1	yes	characteristic
126	C₂×D₄×C₁₉	—	2	4	no	—
127	C₂×D₄×C₁₉	—	2	4	no	—
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	1	no	—
131	C₂×D₄×C₁₉	—	2	1	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	—	2	2	no	—
137	C₂×D₄×C₁₉	—	4	4	no	—
138	C₂×D₄×C₁₉	—	4	4	no	—
139	C₂×D₄×C₁₉	—	4	4	no	—
140	C₂×D₄×C₁₉	—	4	2	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	4	1	no	—
143	C₂×D₄×C₁₉	—	4	1	no	—
144	C₂×D₄×C₁₉	—	4	1	no	—
145	C₂×D₄×C₁₉	—	4	1	no	—
146	C₂×D₄×C₁₉	—	8	2	no	—
147	C₂×D₄×C₁₉	#41	1	4	yes	—
148	C₂²×C₄×C₁₉	—	2	2	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	1	no	—
152	C₂²×C₄×C₁₉	—	2	1	no	—
153	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
159	D₈×C₁₉	—	4	4	no	—
160	D₈×C₁₉	—	4	4	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	—	2	2	no	—
166	M₁₆×C₁₉	—	2	2	no	—
167	M₁₆×C₁₉	—	4	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₂×C₈×C₁₉	—	2	2	no	—
170	C₂×C₈×C₁₉	—	2	2	no	—
171	C₂×C₈×C₁₉	—	2	2	no	—
172	C₂×C₈×C₁₉	—	2	1	no	—
173	C₂×C₈×C₁₉	—	2	1	no	—
174	C₂×C₈×C₁₉	—	4	2	no	—
175	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
176	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
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	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
189	C₂²⋊C₄×C₁₉	—	4	1	no	—
190	C₂²⋊C₄×C₁₉	—	4	1	no	—
191	C₄²×C₁₉	—	2	1	no	—
192	C₄²×C₁₉	—	2	1	no	—
193	C₄²×C₁₉	—	2	1	no	—
194	C₄²×C₁₉	—	2	1	no	—
195	#24520	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₁₉	—	2	2	no	—
197	C₂³×C₁₉	—	2	2	no	—
198	C₂³×C₁₉	—	2	4	no	—
199	C₂³×C₁₉	—	4	1	no	—
200	C₂³×C₁₉	—	4	4	no	—
201	C₂³×C₁₉	—	4	4	no	—
202	C₂³×C₁₉	—	4	2	no	—
203	C₂³×C₁₉	—	4	2	no	—
204	C₂³×C₁₉	—	4	1	no	—
205	C₂³×C₁₉	—	4	2	no	—
206	C₂³×C₁₉	—	8	2	no	—
207	C₂³×C₁₉	—	8	2	no	—
208	C₂³×C₁₉	—	8	2	no	—
209	C₂³×C₁₉	—	8	2	no	—
210	C₂³×C₁₉	—	8	2	no	—
211	C₂³×C₁₉	—	8	1	no	—
212	C₂³×C₁₉	—	8	1	no	—
213	C₂³×C₁₉	—	8	16	no	—
214	C₂³×C₁₉	—	8	2	no	—
215	C₂³×C₁₉	#121	1	1	yes	characteristic
216	C₂³×C₁₉	#121	1	1	yes	characteristic
217	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
218	D₄×C₁₉	—	2	4	no	—
219	D₄×C₁₉	—	2	4	no	—
220	D₄×C₁₉	—	4	4	no	—
221	D₄×C₁₉	—	4	4	no	—
222	D₄×C₁₉	—	4	1	no	—
223	D₄×C₁₉	—	4	2	no	—
224	D₄×C₁₉	—	4	1	no	—
225	D₄×C₁₉	—	4	2	no	—
226	D₄×C₁₉	—	4	2	no	—
227	D₄×C₁₉	—	8	2	no	—
228	D₄×C₁₉	—	8	2	no	—
229	C₂×C₄×C₁₉	—	2	2	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	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	2	no	—
236	C₂×C₄×C₁₉	—	2	1	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	1	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	4	2	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	8	1	no	—
243	C₂×C₄×C₁₉	—	8	1	no	—
244	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
249	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
250	C₈×C₁₉	—	2	2	no	—
251	C₈×C₁₉	—	2	2	no	—
252	C₈×C₁₉	—	4	1	no	—
253	C₈×C₁₉	—	4	2	no	—
254	C₈×C₁₉	—	4	1	no	—
255	C₈×C₁₉	—	4	2	no	—
256	#3094	C₂×C₁₉	1	1	yes	characteristic, complemented
257	C₂×#447	C₂×C₁₉	1	1	yes	characteristic
258	#2924	C₂×C₁₉	1	1	yes	characteristic, complemented
259	C₂×#418	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#2063	C₂×C₁₉	1	2	yes	complemented
261	#2045	C₂×C₁₉	1	2	yes	complemented
262	#1978	C₂×C₁₉	1	2	yes	complemented
263	#1931	C₂×C₁₉	1	2	yes	complemented
264	#1900	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1855	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1783	C₂×C₁₉	1	1	yes	characteristic, complemented
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	2	1	no	—
270	C₂²×C₁₉	—	2	1	no	—
271	C₂²×C₁₉	—	2	1	no	—
272	C₂²×C₁₉	—	2	1	no	—
273	C₂²×C₁₉	—	2	1	no	—
274	C₂²×C₁₉	—	4	4	no	—
275	C₂²×C₁₉	—	4	4	no	—
276	C₂²×C₁₉	—	8	4	no	—
277	C₂²×C₁₉	—	8	4	no	—
278	C₂²×C₁₉	—	8	8	no	—
279	C₂²×C₁₉	—	8	8	no	—
280	C₂²×C₁₉	—	8	2	no	—
281	C₂²×C₁₉	—	8	2	no	—
282	C₂²×C₁₉	—	8	1	no	—
283	C₂²×C₁₉	—	8	1	no	—
284	C₂²×C₁₉	—	8	1	no	—
285	C₂²×C₁₉	—	16	2	no	—
286	C₂²×C₁₉	#472	1	2	yes	—
287	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
288	C₂²×C₁₉	#551	1	2	yes	—
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	4	1	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	1	no	—
295	C₄×C₁₉	—	8	1	no	—
296	C₄×C₁₉	#525	1	1	yes	characteristic
297	C₄×C₁₉	#535	1	1	yes	characteristic
298	C₄×C₁₉	#546	1	2	yes	—
299	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
300	C₂²×D₈	C₂²×C₁₉	1	2	yes	—
301	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
303	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
304	#482	—	2	1	no	—
305	#482	—	2	1	no	—
306	#481	—	2	1	no	—
307	#480	—	2	1	no	—
308	#447	—	2	1	no	—
309	#447	—	2	1	no	—
310	#447	—	2	2	no	—
311	#433	—	2	2	no	—
312	#432	—	2	1	no	—
313	#431	—	2	1	no	—
314	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
315	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
316	#428	C₂²×C₁₉	1	1	yes	characteristic, complemented
317	#424	C₂²×C₁₉	1	2	yes	complemented
318	#418	—	2	1	no	—
319	#418	—	2	1	no	—
320	#418	C₂²×C₁₉	1	2	yes	—
321	#418	C₂²×C₁₉	1	2	yes	—
322	#418	C₂²×C₁₉	1	1	yes	characteristic, complemented
323	#418	C₂²×C₁₉	1	1	yes	characteristic, complemented
324	C₂×#102	—	2	1	no	—
325	C₂×#102	—	2	1	no	—
326	C₂×#102	C₂²×C₁₉	1	2	yes	—
327	C₂×#100	C₂²×C₁₉	1	2	yes	—
328	C₂×#100	C₂²×C₁₉	1	2	yes	—
329	C₂×#100	C₂²×C₁₉	1	2	yes	complemented
330	#407	C₂²×C₁₉	1	1	yes	characteristic
331	#407	C₂²×C₁₉	1	1	yes	characteristic
332	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
333	#405	C₂²×C₁₉	1	2	yes	complemented
334	#343	C₂²×C₁₉	1	2	yes	complemented
335	#341	C₂²×C₁₉	1	2	yes	complemented
336	C₂×C₁₉	—	2	2	no	—
337	C₂×C₁₉	—	2	2	no	—
338	C₂×C₁₉	—	4	1	no	—
339	C₂×C₁₉	—	8	4	no	—
340	C₂×C₁₉	—	16	1	no	—
341	C₂×C₁₉	#2411	1	1	yes	characteristic
342	C₂×C₁₉	C₂×#472	1	1	yes	characteristic
343	C₂×C₁₉	#3068	1	1	yes	characteristic
344	C₂⁵	—	2	1	no	—
345	C₂²×D₄	—	2	4	no	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	2	1	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	—	4	2	no	—
353	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
354	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
355	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×D₈	—	2	4	no	—
357	C₂×D₈	—	2	2	no	—
358	C₂×D₈	—	2	2	no	—
359	C₂×D₈	—	4	2	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	4	2	no	—
362	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
363	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
364	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
365	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	#121	—	2	1	no	—
371	#121	—	2	1	no	—
372	#117	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	D₄×C₁₉	1	1	yes	characteristic
375	#117	D₄×C₁₉	1	1	yes	characteristic
376	#117	C₂³×C₁₉	1	1	yes	characteristic
377	#117	C₂³×C₁₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	#108	—	4	2	no	—
385	#107	—	2	1	no	—
386	#107	—	2	1	no	—
387	#106	—	2	1	no	—
388	#106	—	2	1	no	—
389	C₄⋊C₈	—	2	2	no	—
390	C₄⋊C₈	—	2	2	no	—
391	#102	—	2	2	no	—
392	#102	—	2	2	no	—
393	#102	—	2	2	no	—
394	#102	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	#102	—	2	1	no	—
398	#102	—	2	1	no	—
399	#102	—	2	1	no	—
400	#102	—	2	1	no	—
401	#100	—	2	4	no	—
402	#100	—	4	2	no	—
403	#100	—	4	2	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
409	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
410	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
411	#97	—	2	2	no	—
412	C₄×C₈	—	2	2	no	—
413	C₁₉	#24520	1	1	yes	characteristic, direct product factor, Sylow
414	C₂⁴	—	2	2	no	—
415	C₂⁴	—	2	1	no	—
416	C₂⁴	—	4	4	no	—
417	C₂⁴	—	4	1	no	—
418	C₂⁴	—	4	1	no	—
419	C₂⁴	—	8	2	no	—
420	C₂⁴	—	8	2	no	—
421	C₂⁴	#41×C₁₉	1	1	yes	characteristic
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	—	4	2	no	—
438	C₂×D₄	—	4	1	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	8	2	no	—
443	C₂×D₄	#41×C₁₉	1	4	yes	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
453	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
454	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
455	D₈	—	4	4	no	—
456	D₈	—	4	4	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	2	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	4	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	4	2	no	—
471	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
472	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
478	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
479	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	4	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	8	2	no	—
502	C₂³	—	8	2	no	—
503	C₂³	—	8	2	no	—
504	C₂³	—	8	2	no	—
505	C₂³	—	8	2	no	—
506	C₂³	—	8	1	no	—
507	C₂³	—	8	1	no	—
508	C₂³	—	8	16	no	—
509	C₂³	—	8	2	no	—
510	C₂³	C₁₉×#121	1	1	yes	characteristic
511	C₂³	C₁₉×#121	1	1	yes	characteristic
512	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	4	4	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	2	no	—
522	D₄	—	8	2	no	—
523	D₄	—	8	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	8	1	no	—
538	C₂×C₄	—	8	1	no	—
539	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
540	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
543	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
544	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
545	C₈	—	2	2	no	—
546	C₈	—	2	2	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	2	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	4	no	—
562	C₂²	—	8	8	no	—
563	C₂²	—	8	8	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	16	2	no	—
570	C₂²	C₁₉×#472	1	2	yes	—
571	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
572	C₂²	C₁₉×#551	1	2	yes	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	8	1	no	—
580	C₄	C₁₉×#525	1	1	yes	characteristic
581	C₄	C₁₉×#535	1	1	yes	characteristic
582	C₄	C₁₉×#546	1	2	yes	—
583	C₂	—	2	2	no	—
584	C₂	—	2	2	no	—
585	C₂	—	4	1	no	—
586	C₂	—	8	4	no	—
587	C₂	—	16	1	no	—
588	C₂	C₁₉×#2411	1	1	yes	characteristic
589	C₂	C₂×C₁₉×#472	1	1	yes	characteristic
590	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	C₂×C₁₉×#447	C₂
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×#3094	C₂	semidirect
3. C₁₉×#2924	C₂	semidirect
4. C₂×C₁₉×#418	C₂	semidirect
5. C₁₉×#2063	C₂	semidirect
6. C₁₉×#2045	C₂	semidirect
7. C₁₉×#1978	C₂	semidirect
8. C₁₉×#1931	C₂	semidirect
9. C₁₉×#1900	C₂	semidirect
10. C₁₉×#1855	C₂	semidirect
11. C₁₉×#1783	C₂	semidirect
27. C₂×C₁₉×#108	C₂²	semidirect
28. C₁₉×#428	C₂²	semidirect
29. C₁₉×#428	C₂²	semidirect
30. C₁₉×#424	C₂²	semidirect
35. C₁₉×#418	C₂²	semidirect
36. C₁₉×#418	C₂²	semidirect
42. C₂×C₁₉×#100	C₂²	semidirect
46. C₁₉×#405	C₂²	semidirect
47. C₁₉×#343	C₂²	semidirect
48. C₁₉×#341	C₂²	semidirect
195. #24520	C₁₉	direct (N × H)
256. #3094	C₂×C₁₉	semidirect
258. #2924	C₂×C₁₉	semidirect
259. C₂×#418	C₂×C₁₉	semidirect
260. #2063	C₂×C₁₉	semidirect
261. #2045	C₂×C₁₉	semidirect
262. #1978	C₂×C₁₉	semidirect
263. #1931	C₂×C₁₉	semidirect
264. #1900	C₂×C₁₉	semidirect
265. #1855	C₂×C₁₉	semidirect
266. #1783	C₂×C₁₉	semidirect
314. C₂×#108	C₂²×C₁₉	semidirect
315. #428	C₂²×C₁₉	semidirect
316. #428	C₂²×C₁₉	semidirect
317. #424	C₂²×C₁₉	semidirect
322. #418	C₂²×C₁₉	semidirect
323. #418	C₂²×C₁₉	semidirect
329. C₂×#100	C₂²×C₁₉	semidirect
333. #405	C₂²×C₁₉	semidirect
334. #343	C₂²×C₁₉	semidirect
335. #341	C₂²×C₁₉	semidirect
413. C₁₉	#24520	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×#447	2
C₁₉×#2924	2
C₂×C₁₉×#418	2
C₁₉×#2063	2
C₁₉×#2045	2
C₁₉×#1978	2
C₁₉×#1931	2
C₁₉×#1900	2
C₁₉×#1855	2
C₁₉×#1783	2
#24520	19

Subgroups — C19×#24520 #18030479

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24520 #18030479