Subgroups — C₁₉×#18469 #18024428

Order 4864.

814 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×#3563	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3236	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3232	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2822	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1617	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1615	C₂	1	2	yes	maximal
7	C₁₉×#1611	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1609	C₂	1	2	yes	maximal
9	C₁₉×#1518	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1512	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1470	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#564	—	2	1	no	—
13	C₁₉×#563	—	2	1	no	—
14	C₁₉×#557	—	2	1	no	—
15	C₁₉×#554	—	2	1	no	—
16	C₁₉×#552	—	2	1	no	—
17	C₁₉×#552	—	2	2	no	—
18	C₁₉×#552	—	2	1	no	—
19	C₁₉×#544	—	2	1	no	—
20	C₁₉×#544	C₂²	1	2	yes	—
21	C₁₉×#541	—	2	1	no	—
22	C₁₉×#541	—	2	2	no	—
23	C₁₉×#539	C₂²	1	2	yes	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₁₉×#529	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#125	C₂²	1	1	yes	characteristic
28	C₁₉×#501	—	2	1	no	—
29	C₁₉×#499	—	2	1	no	—
30	C₁₉×#491	—	2	1	no	—
31	C₁₉×#488	—	2	1	no	—
32	C₁₉×#484	C₂²	1	1	yes	characteristic
33	C₁₉×#484	C₂²	1	2	yes	—
34	C₁₉×#483	C₂²	1	1	yes	characteristic
35	C₁₉×#483	C₂²	1	2	yes	—
36	C₁₉×#481	C₂²	1	1	yes	characteristic
37	C₁₉×#480	C₂²	1	1	yes	characteristic
38	C₁₉×#479	—	2	1	no	—
39	C₁₉×#479	—	2	2	no	—
40	C₁₉×#478	—	2	1	no	—
41	C₁₉×#432	C₂²	1	1	yes	characteristic
42	C₁₉×#431	C₂²	1	1	yes	characteristic
43	C₁₉×#400	—	2	1	no	—
44	C₁₉×#400	C₂²	1	2	yes	—
45	C₁₉×#398	—	2	2	no	—
46	C₁₉×#398	—	2	1	no	—
47	C₁₉×#398	C₂²	1	2	yes	—
48	C₁₉×#382	C₂²	1	1	yes	characteristic
49	C₁₉×#328	C₂²	1	2	yes	—
50	C₁₉×#328	C₂²	1	2	yes	—
51	C₁₉×#328	C₂²	1	2	yes	—
52	C₁₉×#327	C₂²	1	2	yes	—
53	C₁₉×#324	C₂²	1	2	yes	—
54	C₁₉×#324	C₂²	1	2	yes	—
55	C₁₉×C₄⋊Q₈	—	2	1	no	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#126	—	2	2	no	—
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#126	—	2	1	no	—
65	C₁₉×#125	—	2	2	no	—
66	C₁₉×#125	—	2	2	no	—
67	C₁₉×#125	—	2	2	no	—
68	C₁₉×#125	—	2	2	no	—
69	C₁₉×#125	—	2	1	no	—
70	C₁₉×#125	—	2	2	no	—
71	C₁₉×#125	—	2	2	no	—
72	C₁₉×#125	—	2	2	no	—
73	C₁₉×#125	—	2	2	no	—
74	C₁₉×#125	—	2	1	no	—
75	C₁₉×#125	—	2	1	no	—
76	C₁₉×#125	—	2	1	no	—
77	C₁₉×#125	—	2	1	no	—
78	C₁₉×#125	—	2	1	no	—
79	C₁₉×#125	—	2	1	no	—
80	C₁₉×#125	—	2	1	no	—
81	C₁₉×#125	—	2	1	no	—
82	C₁₉×#125	—	2	1	no	—
83	C₁₉×#125	D₄	1	1	yes	characteristic
84	C₁₉×#124	D₄	1	1	yes	characteristic
85	C₁₉×#123	—	2	2	no	—
86	C₁₉×#123	—	2	1	no	—
87	C₁₉×#123	—	2	2	no	—
88	C₁₉×C₂²⋊Q₈	—	2	1	no	—
89	C₁₉×C₂²⋊Q₈	—	2	1	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	2	no	—
92	C₁₉×C₂²⋊Q₈	—	2	2	no	—
93	C₁₉×C₂²⋊Q₈	—	2	1	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
96	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
97	C₁₉×#121	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₁₉	—	2	1	no	—
99	C₄×Q₈×C₁₉	—	2	2	no	—
100	C₄×Q₈×C₁₉	—	2	1	no	—
101	C₄×Q₈×C₁₉	—	2	1	no	—
102	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
103	C₄×Q₈×C₁₉	D₄	1	2	yes	—
104	C₄×D₄×C₁₉	—	2	1	no	—
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
107	C₁₉×#117	—	2	2	no	—
108	C₁₉×#117	—	2	1	no	—
109	C₁₉×#117	—	2	1	no	—
110	C₁₉×#117	—	2	2	no	—
111	C₁₉×#117	—	2	1	no	—
112	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
116	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
120	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
124	C₁₉×#107	—	2	1	no	—
125	C₁₉×#107	—	2	1	no	—
126	C₁₉×#107	—	2	2	no	—
127	C₁₉×#106	—	2	1	no	—
128	C₁₉×#106	—	2	1	no	—
129	C₁₉×#106	—	2	2	no	—
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×#103	—	2	1	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#103	—	2	1	no	—
135	C₁₉×#103	—	2	2	no	—
136	C₁₉×#102	—	2	1	no	—
137	C₁₉×#102	—	2	1	no	—
138	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
139	C₁₉×C₂²⋊C₈	C₂³	1	1	yes	characteristic
140	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
141	C₁₉×#97	—	2	1	no	—
142	C₄×C₈×C₁₉	—	2	1	no	—
143	C₁₉×#95	—	2	1	no	—
144	C₁₉×#95	—	2	2	no	—
145	C₁₉×#95	—	2	2	no	—
146	C₁₉×#95	—	2	2	no	—
147	C₁₉×#95	C₂³	1	2	yes	—
148	C₂×Q₈×C₁₉	—	2	2	no	—
149	C₂×Q₈×C₁₉	—	2	1	no	—
150	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
151	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	—	2	1	no	—
153	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	1	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₁₉	—	2	1	no	—
165	C₂×C₈×C₁₉	—	2	1	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₄⋊C₄×C₁₉	—	2	2	no	—
168	C₄⋊C₄×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	2	no	—
174	C₄⋊C₄×C₁₉	—	2	2	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	—	2	2	no	—
179	C₄⋊C₄×C₁₉	—	2	1	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	1	no	—
182	C₄⋊C₄×C₁₉	—	2	1	no	—
183	C₄⋊C₄×C₁₉	—	2	1	no	—
184	C₄⋊C₄×C₁₉	—	2	1	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	2	2	no	—
190	C₄⋊C₄×C₁₉	—	2	1	no	—
191	C₄⋊C₄×C₁₉	—	2	2	no	—
192	C₄⋊C₄×C₁₉	—	2	1	no	—
193	C₄⋊C₄×C₁₉	—	2	1	no	—
194	C₄⋊C₄×C₁₉	—	2	1	no	—
195	C₄⋊C₄×C₁₉	—	2	1	no	—
196	C₄⋊C₄×C₁₉	—	4	1	no	—
197	C₄⋊C₄×C₁₉	—	4	1	no	—
198	C₄⋊C₄×C₁₉	—	4	1	no	—
199	C₄⋊C₄×C₁₉	—	4	1	no	—
200	C₄⋊C₄×C₁₉	—	8	1	no	—
201	C₄⋊C₄×C₁₉	—	8	2	no	—
202	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
203	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
205	C₂²⋊C₄×C₁₉	—	2	2	no	—
206	C₂²⋊C₄×C₁₉	—	2	2	no	—
207	C₂²⋊C₄×C₁₉	—	2	2	no	—
208	C₂²⋊C₄×C₁₉	—	2	2	no	—
209	C₂²⋊C₄×C₁₉	—	2	1	no	—
210	C₂²⋊C₄×C₁₉	—	2	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	1	no	—
212	C₂²⋊C₄×C₁₉	—	2	1	no	—
213	C₂²⋊C₄×C₁₉	—	2	1	no	—
214	C₄²×C₁₉	—	2	2	no	—
215	C₄²×C₁₉	—	2	2	no	—
216	C₄²×C₁₉	—	2	2	no	—
217	C₄²×C₁₉	—	2	2	no	—
218	C₄²×C₁₉	—	2	1	no	—
219	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
223	#18469	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂³×C₁₉	—	2	1	no	—
225	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₁₉	—	4	1	no	—
227	Q₈×C₁₉	—	4	2	no	—
228	Q₈×C₁₉	—	4	2	no	—
229	Q₈×C₁₉	—	8	2	no	—
230	D₄×C₁₉	—	4	1	no	—
231	D₄×C₁₉	—	4	1	no	—
232	D₄×C₁₉	—	4	1	no	—
233	C₂×C₄×C₁₉	—	2	1	no	—
234	C₂×C₄×C₁₉	—	2	1	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	2	no	—
239	C₂×C₄×C₁₉	—	2	1	no	—
240	C₂×C₄×C₁₉	—	2	2	no	—
241	C₂×C₄×C₁₉	—	2	2	no	—
242	C₂×C₄×C₁₉	—	2	2	no	—
243	C₂×C₄×C₁₉	—	2	2	no	—
244	C₂×C₄×C₁₉	—	4	1	no	—
245	C₂×C₄×C₁₉	—	4	1	no	—
246	C₂×C₄×C₁₉	—	4	2	no	—
247	C₂×C₄×C₁₉	—	4	2	no	—
248	C₂×C₄×C₁₉	—	4	2	no	—
249	C₂×C₄×C₁₉	—	4	2	no	—
250	C₂×C₄×C₁₉	—	4	2	no	—
251	C₂×C₄×C₁₉	—	4	1	no	—
252	C₂×C₄×C₁₉	—	4	1	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	4	1	no	—
255	C₂×C₄×C₁₉	—	4	1	no	—
256	C₂×C₄×C₁₉	—	8	2	no	—
257	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
258	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
263	C₈×C₁₉	—	4	1	no	—
264	C₈×C₁₉	—	4	1	no	—
265	C₈×C₁₉	—	4	2	no	—
266	#3563	C₂×C₁₉	1	1	yes	characteristic
267	#3236	C₂×C₁₉	1	1	yes	characteristic, complemented
268	#3232	C₂×C₁₉	1	1	yes	characteristic
269	#2822	C₂×C₁₉	1	1	yes	characteristic, complemented
270	#1617	C₂×C₁₉	1	2	yes	complemented
271	#1615	C₂×C₁₉	1	2	yes	—
272	#1611	C₂×C₁₉	1	2	yes	complemented
273	#1609	C₂×C₁₉	1	2	yes	—
274	#1518	C₂×C₁₉	1	1	yes	characteristic, complemented
275	#1512	C₂×C₁₉	1	1	yes	characteristic
276	#1470	C₂×C₁₉	1	1	yes	characteristic, complemented
277	C₂²×C₁₉	—	2	1	no	—
278	C₂²×C₁₉	—	2	1	no	—
279	C₂²×C₁₉	—	4	1	no	—
280	C₂²×C₁₉	—	4	1	no	—
281	C₂²×C₁₉	—	4	1	no	—
282	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
283	C₂²×C₁₉	#577	1	1	yes	characteristic
284	C₂²×C₁₉	#578	1	1	yes	characteristic
285	C₄×C₁₉	—	2	1	no	—
286	C₄×C₁₉	—	2	1	no	—
287	C₄×C₁₉	—	2	1	no	—
288	C₄×C₁₉	—	2	1	no	—
289	C₄×C₁₉	—	2	1	no	—
290	C₄×C₁₉	—	2	1	no	—
291	C₄×C₁₉	—	4	2	no	—
292	C₄×C₁₉	—	4	1	no	—
293	C₄×C₁₉	—	4	1	no	—
294	C₄×C₁₉	—	4	2	no	—
295	C₄×C₁₉	—	4	2	no	—
296	C₄×C₁₉	—	4	2	no	—
297	C₄×C₁₉	—	4	1	no	—
298	C₄×C₁₉	—	8	2	no	—
299	C₄×C₁₉	—	8	1	no	—
300	C₄×C₁₉	—	8	1	no	—
301	#564	—	2	1	no	—
302	#563	—	2	1	no	—
303	#557	—	2	1	no	—
304	#554	—	2	1	no	—
305	#552	—	2	1	no	—
306	#552	—	2	2	no	—
307	#552	—	2	1	no	—
308	#544	—	2	1	no	—
309	#544	C₂²×C₁₉	1	2	yes	—
310	#541	—	2	1	no	—
311	#541	—	2	2	no	—
312	#539	C₂²×C₁₉	1	2	yes	—
313	#533	C₂²×C₁₉	1	1	yes	characteristic
314	#529	C₂²×C₁₉	1	1	yes	characteristic
315	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
316	C₂×#125	C₂²×C₁₉	1	1	yes	characteristic
317	#501	—	2	1	no	—
318	#499	—	2	1	no	—
319	#491	—	2	1	no	—
320	#488	—	2	1	no	—
321	#484	C₂²×C₁₉	1	2	yes	—
322	#484	C₂²×C₁₉	1	1	yes	characteristic
323	#483	C₂²×C₁₉	1	2	yes	—
324	#483	C₂²×C₁₉	1	1	yes	characteristic
325	#481	C₂²×C₁₉	1	1	yes	characteristic
326	#480	C₂²×C₁₉	1	1	yes	characteristic
327	#479	—	2	1	no	—
328	#479	—	2	2	no	—
329	#478	—	2	1	no	—
330	#432	C₂²×C₁₉	1	1	yes	characteristic
331	#431	C₂²×C₁₉	1	1	yes	characteristic
332	#400	—	2	1	no	—
333	#400	C₂²×C₁₉	1	2	yes	—
334	#398	—	2	1	no	—
335	#398	—	2	2	no	—
336	#398	C₂²×C₁₉	1	2	yes	—
337	#382	C₂²×C₁₉	1	1	yes	characteristic
338	#328	C₂²×C₁₉	1	2	yes	—
339	#328	C₂²×C₁₉	1	2	yes	—
340	#328	C₂²×C₁₉	1	2	yes	—
341	#327	C₂²×C₁₉	1	2	yes	—
342	#324	C₂²×C₁₉	1	2	yes	—
343	#324	C₂²×C₁₉	1	2	yes	—
344	C₂×C₁₉	—	2	1	no	—
345	C₂×C₁₉	—	2	1	no	—
346	C₂×C₁₉	—	8	1	no	—
347	C₂×C₁₉	#3013	1	1	yes	characteristic
348	C₂×C₁₉	#3020	1	1	yes	characteristic
349	C₂×C₁₉	#3028	1	1	yes	characteristic
350	C₄⋊Q₈	—	2	1	no	—
351	C₄⋊Q₈	—	2	2	no	—
352	C₄⋊Q₈	—	2	2	no	—
353	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
354	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
355	#126	—	2	2	no	—
356	#126	—	2	2	no	—
357	#126	—	2	2	no	—
358	#126	—	2	2	no	—
359	#126	—	2	1	no	—
360	#125	—	2	2	no	—
361	#125	—	2	2	no	—
362	#125	—	2	2	no	—
363	#125	—	2	2	no	—
364	#125	—	2	1	no	—
365	#125	—	2	2	no	—
366	#125	—	2	2	no	—
367	#125	—	2	2	no	—
368	#125	—	2	2	no	—
369	#125	—	2	1	no	—
370	#125	—	2	1	no	—
371	#125	—	2	1	no	—
372	#125	—	2	1	no	—
373	#125	—	2	1	no	—
374	#125	—	2	1	no	—
375	#125	—	2	1	no	—
376	#125	—	2	1	no	—
377	#125	—	2	1	no	—
378	#125	D₄×C₁₉	1	1	yes	characteristic
379	#124	D₄×C₁₉	1	1	yes	characteristic
380	#123	—	2	2	no	—
381	#123	—	2	1	no	—
382	#123	—	2	2	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	2	1	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
391	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
392	#121	C₂³×C₁₉	1	1	yes	characteristic
393	C₄×Q₈	—	2	1	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	1	no	—
396	C₄×Q₈	—	2	1	no	—
397	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
398	C₄×Q₈	D₄×C₁₉	1	2	yes	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
402	#117	—	2	2	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	—	2	2	no	—
406	#117	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	2	no	—
412	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
414	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
418	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
419	#107	—	2	1	no	—
420	#107	—	2	1	no	—
421	#107	—	2	2	no	—
422	#106	—	2	1	no	—
423	#106	—	2	1	no	—
424	#106	—	2	2	no	—
425	C₄⋊C₈	—	2	1	no	—
426	C₄⋊C₈	—	2	1	no	—
427	#103	—	2	1	no	—
428	#103	—	2	2	no	—
429	#103	—	2	1	no	—
430	#103	—	2	2	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
434	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
435	C₂²⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
436	#97	—	2	1	no	—
437	C₄×C₈	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	2	no	—
440	#95	—	2	2	no	—
441	#95	—	2	2	no	—
442	#95	C₂³×C₁₉	1	2	yes	—
443	C₁₉	#18469	1	1	yes	characteristic, direct product factor, Sylow
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
447	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
458	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	8	1	no	—
497	C₄⋊C₄	—	8	2	no	—
498	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
499	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	1	no	—
508	C₂²⋊C₄	—	2	1	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	2	2	no	—
514	C₄²	—	2	1	no	—
515	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
516	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
518	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
519	C₂³	—	2	1	no	—
520	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
521	Q₈	—	4	1	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	8	2	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	D₄	—	4	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	8	2	no	—
552	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
553	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
554	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
555	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
557	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	2	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
567	C₂²	C₁₉×#577	1	1	yes	characteristic
568	C₂²	C₁₉×#578	1	1	yes	characteristic
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	2	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	8	2	no	—
583	C₄	—	8	1	no	—
584	C₄	—	8	1	no	—
585	C₂	—	2	1	no	—
586	C₂	—	2	1	no	—
587	C₂	—	8	1	no	—
588	C₂	C₁₉×#3013	1	1	yes	characteristic
589	C₂	C₁₉×#3020	1	1	yes	characteristic
590	C₂	C₁₉×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#121	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3236	C₂	semidirect
4. C₁₉×#2822	C₂	semidirect
5. C₁₉×#1617	C₂	semidirect
7. C₁₉×#1611	C₂	semidirect
9. C₁₉×#1518	C₂	semidirect
11. C₁₉×#1470	C₂	semidirect
223. #18469	C₁₉	direct (N × H)
267. #3236	C₂×C₁₉	semidirect
269. #2822	C₂×C₁₉	semidirect
270. #1617	C₂×C₁₉	semidirect
272. #1611	C₂×C₁₉	semidirect
274. #1518	C₂×C₁₉	semidirect
276. #1470	C₂×C₁₉	semidirect
443. C₁₉	#18469	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×#3563	2
C₁₉×#3236	2
C₁₉×#3232	2
C₁₉×#2822	2
C₁₉×#1617	2
C₁₉×#1615	2
C₁₉×#1611	2
C₁₉×#1609	2
C₁₉×#1518	2
C₁₉×#1512	2
C₁₉×#1470	2
#18469	19

Subgroups — C19×#18469 #18024428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#18469 #18024428