Subgroups — C₁₉×#23590 #18029549

Order 4864.

1074 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3461	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉×#137	C₂	1	2	yes	maximal, complemented
3	C₄×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2060	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2039	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2038	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2028	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2007	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#2005	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₉×#104	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#137	C₂²	1	2	yes	—
13	C₁₉×#544	C₂²	1	1	yes	characteristic
14	C₁₉×#542	—	2	2	no	—
15	C₁₉×#541	—	2	2	no	—
16	C₁₉×#539	—	2	2	no	—
17	C₁₉×#537	C₂²	1	1	yes	characteristic
18	C₁₉×#536	C₂²	1	2	yes	—
19	C₁₉×#533	—	2	2	no	—
20	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₉×#529	—	2	2	no	—
22	C₁₉×#529	—	2	2	no	—
23	C₄×#41×C₁₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#441	—	2	2	no	—
27	C₁₉×#440	—	2	2	no	—
28	C₄×Q₁₆×C₁₉	—	2	2	no	—
29	C₄×SD₁₆×C₁₉	—	2	2	no	—
30	C₁₉×#428	C₂²	1	2	yes	—
31	C₂×C₁₉×#104	C₂²	1	2	yes	—
32	C₂×C₁₉×#104	C₂²	1	2	yes	—
33	C₁₉×#419	C₂²	1	2	yes	—
34	C₁₉×#417	C₂²	1	2	yes	—
35	C₂×C₁₉×#101	C₂²	1	2	yes	—
36	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
37	C₁₉×#391	C₂²	1	1	yes	characteristic
38	C₁₉×#391	C₂²	1	1	yes	characteristic
39	C₁₉×#389	—	2	2	no	—
40	C₁₉×#384	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
42	C₄³×C₁₉	C₂²	1	1	yes	characteristic
43	C₁₉×#343	C₂²	1	1	yes	characteristic
44	C₁₉×#343	C₂²	1	1	yes	characteristic
45	C₁₉×#339	C₂²	1	2	yes	—
46	C₁₉×#339	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×#137	—	2	4	no	—
51	C₁₉×#137	—	2	4	no	—
52	C₂×Q₁₆×C₁₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
55	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×C₄⋊Q₈	—	2	2	no	—
58	C₁₉×C₄⋊Q₈	—	2	2	no	—
59	C₁₉×C₄⋊Q₈	—	2	2	no	—
60	C₁₉×#126	—	2	4	no	—
61	C₁₉×#126	—	2	4	no	—
62	C₁₉×#125	—	2	2	no	—
63	C₁₉×#125	—	2	4	no	—
64	C₁₉×#125	—	2	2	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#124	—	2	2	no	—
67	C₁₉×#123	—	2	4	no	—
68	C₁₉×#123	—	2	4	no	—
69	C₁₉×C₂²⋊Q₈	—	2	4	no	—
70	C₁₉×C₂²⋊Q₈	—	2	2	no	—
71	C₁₉×C₂²⋊Q₈	—	2	2	no	—
72	C₁₉×C₂²⋊Q₈	—	2	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	2	no	—
74	C₁₉×#121	—	2	2	no	—
75	C₁₉×#121	—	2	2	no	—
76	C₄×Q₈×C₁₉	—	2	2	no	—
77	C₄×Q₈×C₁₉	—	2	2	no	—
78	C₄×Q₈×C₁₉	—	2	2	no	—
79	C₄×Q₈×C₁₉	—	2	2	no	—
80	C₄×Q₈×C₁₉	—	2	2	no	—
81	C₄×Q₈×C₁₉	D₄	1	2	yes	—
82	C₄×Q₈×C₁₉	D₄	1	2	yes	—
83	C₄×D₄×C₁₉	—	2	2	no	—
84	C₄×D₄×C₁₉	—	2	2	no	—
85	C₄×D₄×C₁₉	—	2	2	no	—
86	C₄×D₄×C₁₉	D₄	1	2	yes	—
87	C₄×D₄×C₁₉	D₄	1	2	yes	—
88	C₁₉×#117	—	2	4	no	—
89	C₁₉×#117	—	2	2	no	—
90	C₁₉×#117	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
95	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₉	—	2	1	no	—
98	C₂×C₄²×C₁₉	—	2	2	no	—
99	C₂×C₄²×C₁₉	—	2	1	no	—
100	C₂×C₄²×C₁₉	—	2	1	no	—
101	C₂×C₄²×C₁₉	D₄	1	2	yes	—
102	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
105	C₁₉×#107	—	2	2	no	—
106	C₁₉×#106	—	2	2	no	—
107	C₁₉×#104	—	2	4	no	—
108	C₁₉×#104	—	2	4	no	—
109	C₁₉×#103	—	2	2	no	—
110	C₁₉×#103	—	2	2	no	—
111	C₁₉×#103	—	2	2	no	—
112	C₁₉×#102	—	2	2	no	—
113	C₁₉×#101	—	2	4	no	—
114	C₁₉×#97	—	2	2	no	—
115	C₄×C₈×C₁₉	—	2	2	no	—
116	C₁₉×#95	—	2	2	no	—
117	C₁₉×#95	—	2	2	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	—	2	2	no	—
124	C₂×Q₈×C₁₉	—	2	1	no	—
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×Q₈×C₁₉	—	2	2	no	—
130	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
131	C₂×Q₈×C₁₉	#41	1	2	yes	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₉	—	2	1	no	—
136	C₂²×C₄×C₁₉	—	2	1	no	—
137	C₂²×C₄×C₁₉	—	2	1	no	—
138	C₂²×C₄×C₁₉	—	2	2	no	—
139	C₂²×C₄×C₁₉	—	2	2	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	1	no	—
142	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
147	Q₁₆×C₁₉	—	2	8	no	—
148	SD₁₆×C₁₉	—	2	8	no	—
149	M₁₆×C₁₉	—	2	2	no	—
150	M₁₆×C₁₉	—	2	2	no	—
151	M₁₆×C₁₉	—	2	2	no	—
152	M₁₆×C₁₉	#41	1	4	yes	—
153	C₂×C₈×C₁₉	—	2	2	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	8	no	—
156	C₄⋊C₄×C₁₉	—	2	4	no	—
157	C₄⋊C₄×C₁₉	—	2	4	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	4	no	—
161	C₄⋊C₄×C₁₉	—	2	4	no	—
162	C₄⋊C₄×C₁₉	—	2	2	no	—
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	2	2	no	—
166	C₄⋊C₄×C₁₉	—	4	4	no	—
167	C₄⋊C₄×C₁₉	—	4	2	no	—
168	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₁₉	—	2	4	no	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₄²×C₁₉	—	2	4	no	—
177	C₄²×C₁₉	—	2	2	no	—
178	C₄²×C₁₉	—	2	2	no	—
179	C₄²×C₁₉	—	2	2	no	—
180	C₄²×C₁₉	—	2	2	no	—
181	C₄²×C₁₉	—	2	2	no	—
182	C₄²×C₁₉	—	2	1	no	—
183	C₄²×C₁₉	—	2	2	no	—
184	C₄²×C₁₉	—	4	2	no	—
185	C₄²×C₁₉	—	4	1	no	—
186	C₄²×C₁₉	—	4	1	no	—
187	C₄²×C₁₉	C₂×D₄	1	2	yes	—
188	C₄²×C₁₉	C₂×D₄	1	2	yes	—
189	C₄²×C₁₉	#41	1	2	yes	—
190	#23590	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂³×C₁₉	—	2	2	no	—
192	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
193	Q₈×C₁₉	—	2	4	no	—
194	Q₈×C₁₉	—	2	2	no	—
195	Q₈×C₁₉	—	2	2	no	—
196	Q₈×C₁₉	—	4	2	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	8	2	no	—
200	D₄×C₁₉	—	2	2	no	—
201	D₄×C₁₉	—	2	2	no	—
202	D₄×C₁₉	—	4	2	no	—
203	D₄×C₁₉	—	4	2	no	—
204	D₄×C₁₉	—	8	2	no	—
205	C₂×C₄×C₁₉	—	2	2	no	—
206	C₂×C₄×C₁₉	—	2	2	no	—
207	C₂×C₄×C₁₉	—	2	2	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	2	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	2	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	—	4	1	no	—
221	C₂×C₄×C₁₉	—	4	1	no	—
222	C₂×C₄×C₁₉	—	4	1	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	4	2	no	—
225	C₂×C₄×C₁₉	—	4	4	no	—
226	C₂×C₄×C₁₉	—	4	2	no	—
227	C₂×C₄×C₁₉	—	4	2	no	—
228	C₂×C₄×C₁₉	—	4	1	no	—
229	C₂×C₄×C₁₉	—	8	2	no	—
230	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
231	C₂×C₄×C₁₉	#120	1	2	yes	—
232	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
233	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
236	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
237	C₈×C₁₉	—	2	4	no	—
238	C₈×C₁₉	—	4	2	no	—
239	#3461	C₂×C₁₉	1	1	yes	characteristic
240	C₄×#137	C₂×C₁₉	1	2	yes	complemented
241	C₄×C₄⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
242	#2060	C₂×C₁₉	1	1	yes	characteristic, complemented
243	#2039	C₂×C₁₉	1	1	yes	characteristic
244	#2038	C₂×C₁₉	1	2	yes	complemented
245	#2028	C₂×C₁₉	1	1	yes	characteristic, complemented
246	#2007	C₂×C₁₉	1	1	yes	characteristic
247	#2005	C₂×C₁₉	1	2	yes	complemented
248	C₄×#104	C₂×C₁₉	1	2	yes	complemented
249	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
250	C₂²×C₁₉	—	2	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	4	2	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	2	no	—
255	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
256	C₂²×C₁₉	#525	1	1	yes	characteristic
257	C₂²×C₁₉	#532	1	1	yes	characteristic
258	C₄×C₁₉	—	2	4	no	—
259	C₄×C₁₉	—	2	1	no	—
260	C₄×C₁₉	—	2	2	no	—
261	C₄×C₁₉	—	4	2	no	—
262	C₄×C₁₉	—	4	2	no	—
263	C₄×C₁₉	—	4	2	no	—
264	C₄×C₁₉	—	4	2	no	—
265	C₄×C₁₉	—	4	2	no	—
266	C₄×C₁₉	—	4	2	no	—
267	C₄×C₁₉	—	4	2	no	—
268	C₄×C₁₉	—	8	1	no	—
269	C₄×C₁₉	#456	1	2	yes	—
270	C₄×C₁₉	#525	1	2	yes	—
271	C₄×C₁₉	#532	1	2	yes	—
272	C₂×#137	C₂²×C₁₉	1	2	yes	—
273	#544	C₂²×C₁₉	1	1	yes	characteristic
274	#542	—	2	2	no	—
275	#541	—	2	2	no	—
276	#539	—	2	2	no	—
277	#537	C₂²×C₁₉	1	1	yes	characteristic
278	#536	C₂²×C₁₉	1	2	yes	—
279	#533	—	2	2	no	—
280	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
281	#529	—	2	2	no	—
282	#529	—	2	2	no	—
283	C₄×#41	C₂²×C₁₉	1	2	yes	—
284	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
285	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
286	#441	—	2	2	no	—
287	#440	—	2	2	no	—
288	C₄×Q₁₆	—	2	2	no	—
289	C₄×SD₁₆	—	2	2	no	—
290	#428	C₂²×C₁₉	1	2	yes	—
291	C₂×#104	C₂²×C₁₉	1	2	yes	—
292	C₂×#104	C₂²×C₁₉	1	2	yes	—
293	#419	C₂²×C₁₉	1	2	yes	—
294	#417	C₂²×C₁₉	1	2	yes	—
295	C₂×#101	C₂²×C₁₉	1	2	yes	—
296	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
297	#391	C₂²×C₁₉	1	1	yes	characteristic
298	#391	C₂²×C₁₉	1	1	yes	characteristic
299	#389	—	2	2	no	—
300	#384	C₂²×C₁₉	1	1	yes	characteristic
301	C₄×C₄⋊C₄	—	2	2	no	—
302	C₄³	C₂²×C₁₉	1	1	yes	characteristic
303	#343	C₂²×C₁₉	1	1	yes	characteristic
304	#343	C₂²×C₁₉	1	1	yes	characteristic
305	#339	C₂²×C₁₉	1	2	yes	—
306	#339	C₂²×C₁₉	1	2	yes	—
307	C₂×C₁₉	—	2	1	no	—
308	C₂×C₁₉	—	2	1	no	—
309	C₂×C₁₉	—	8	2	no	—
310	C₂×C₁₉	#2388	1	1	yes	characteristic
311	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
312	C₂×C₁₉	#3018	1	1	yes	characteristic
313	C₂×#41	C₂³×C₁₉	1	2	yes	—
314	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
315	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
316	#137	—	2	4	no	—
317	#137	—	2	4	no	—
318	C₂×Q₁₆	—	2	2	no	—
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
321	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	—	2	2	no	—
326	#126	—	2	4	no	—
327	#126	—	2	4	no	—
328	#125	—	2	2	no	—
329	#125	—	2	4	no	—
330	#125	—	2	2	no	—
331	#124	—	2	2	no	—
332	#124	—	2	2	no	—
333	#123	—	2	4	no	—
334	#123	—	2	4	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₂²⋊Q₈	—	2	2	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	2	2	no	—
340	#121	—	2	2	no	—
341	#121	—	2	2	no	—
342	C₄×Q₈	—	2	2	no	—
343	C₄×Q₈	—	2	2	no	—
344	C₄×Q₈	—	2	2	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	D₄×C₁₉	1	2	yes	—
348	C₄×Q₈	D₄×C₁₉	1	2	yes	—
349	C₄×D₄	—	2	2	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	D₄×C₁₉	1	2	yes	—
353	C₄×D₄	D₄×C₁₉	1	2	yes	—
354	#117	—	2	4	no	—
355	#117	—	2	2	no	—
356	#117	C₂³×C₁₉	1	2	yes	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	D₄×C₁₉	1	2	yes	—
368	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
371	#107	—	2	2	no	—
372	#106	—	2	2	no	—
373	#104	—	2	4	no	—
374	#104	—	2	4	no	—
375	#103	—	2	2	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#102	—	2	2	no	—
379	#101	—	2	4	no	—
380	#97	—	2	2	no	—
381	C₄×C₈	—	2	2	no	—
382	#95	—	2	2	no	—
383	#95	—	2	2	no	—
384	C₁₉	#23590	1	1	yes	characteristic, direct product factor, Sylow
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
398	C₂×Q₈	#41×C₁₉	1	2	yes	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
414	Q₁₆	—	2	8	no	—
415	SD₁₆	—	2	8	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	#41×C₁₉	1	4	yes	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	4	4	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
436	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	4	2	no	—
452	C₄²	—	4	1	no	—
453	C₄²	—	4	1	no	—
454	C₄²	C₂×D₄×C₁₉	1	2	yes	—
455	C₄²	C₂×D₄×C₁₉	1	2	yes	—
456	C₄²	#41×C₁₉	1	2	yes	—
457	C₂³	—	2	2	no	—
458	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
459	Q₈	—	2	4	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	8	2	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	8	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	8	2	no	—
496	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
497	C₂×C₄	C₁₉×#120	1	2	yes	—
498	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
500	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
501	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
502	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
503	C₈	—	2	4	no	—
504	C₈	—	4	2	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	1	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
511	C₂²	C₁₉×#525	1	1	yes	characteristic
512	C₂²	C₁₉×#532	1	1	yes	characteristic
513	C₄	—	2	4	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	2	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	8	1	no	—
524	C₄	C₁₉×#456	1	2	yes	—
525	C₄	C₁₉×#525	1	2	yes	—
526	C₄	C₁₉×#532	1	2	yes	—
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	8	2	no	—
530	C₂	C₁₉×#2388	1	1	yes	characteristic
531	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
532	C₂	C₁₉×#3018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂×#120
prime radical	C₁₉×#537	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₉×#137	C₂	semidirect
3. C₄×C₁₉×C₄⋊Q₈	C₂	semidirect
4. C₁₉×#2060	C₂	semidirect
6. C₁₉×#2038	C₂	semidirect
7. C₁₉×#2028	C₂	semidirect
9. C₁₉×#2005	C₂	semidirect
10. C₄×C₁₉×#104	C₂	semidirect
11. C₄×C₁₉×#101	C₂	semidirect
190. #23590	C₁₉	direct (N × H)
240. C₄×#137	C₂×C₁₉	semidirect
241. C₄×C₄⋊Q₈	C₂×C₁₉	semidirect
242. #2060	C₂×C₁₉	semidirect
244. #2038	C₂×C₁₉	semidirect
245. #2028	C₂×C₁₉	semidirect
247. #2005	C₂×C₁₉	semidirect
248. C₄×#104	C₂×C₁₉	semidirect
249. C₄×#101	C₂×C₁₉	semidirect
384. C₁₉	#23590	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×#3461	2
C₄×C₁₉×#137	2
C₄×C₁₉×C₄⋊Q₈	2
C₁₉×#2060	2
C₁₉×#2039	2
C₁₉×#2038	2
C₁₉×#2028	2
C₁₉×#2007	2
C₁₉×#2005	2
C₄×C₁₉×#104	2
C₄×C₁₉×#101	2
#23590	19

Subgroups — C19×#23590 #18029549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23590 #18029549