Subgroups — C₁₉×#17617 #18023576

Order 4864.

1018 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3506	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2972	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2357	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1517	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1516	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1503	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1502	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1501	C₂	1	4	yes	maximal, complemented
10	C₁₉×#559	—	2	2	no	—
11	C₁₉×#556	C₄	1	2	yes	complemented
12	C₁₉×#555	C₄	1	2	yes	complemented
13	C₁₉×#553	—	2	2	no	—
14	C₁₉×#550	C₄	1	2	yes	complemented
15	C₁₉×#547	C₄	1	2	yes	complemented
16	C₁₉×#538	—	2	2	no	—
17	C₁₉×#535	—	2	1	no	—
18	C₁₉×#533	C₂²	1	1	yes	characteristic
19	C₁₉×#532	C₂²	1	1	yes	characteristic
20	C₁₉×#525	C₂²	1	4	yes	—
21	C₁₉×#520	—	2	1	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₈×D₄×C₁₉	—	2	2	no	—
24	C₈×D₄×C₁₉	—	2	2	no	—
25	C₁₉×#431	C₂²	1	1	yes	characteristic
26	C₁₉×#431	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
28	C₁₉×#390	—	2	1	no	—
29	C₁₉×#388	—	2	2	no	—
30	C₁₉×#382	C₂²	1	1	yes	characteristic
31	C₁₉×#381	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
35	C₁₉×#328	C₂²	1	2	yes	—
36	C₁₉×#328	C₂²	1	4	yes	—
37	C₁₉×#328	C₂²	1	2	yes	—
38	C₁₉×#327	C₂²	1	2	yes	—
39	C₁₉×#327	C₂²	1	4	yes	—
40	C₁₉×#327	C₂²	1	2	yes	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	C₂×C₄	1	4	yes	—
43	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₉	—	2	4	no	—
46	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
47	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
48	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₉×#127	—	2	2	no	—
50	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
51	C₁₉×#126	—	2	4	no	—
52	C₁₉×#125	—	2	1	no	—
53	C₁₉×#124	—	2	2	no	—
54	C₁₉×#124	—	2	4	no	—
55	C₁₉×#124	—	2	1	no	—
56	C₁₉×#123	—	2	4	no	—
57	C₁₉×#123	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	2	1	no	—
59	C₁₉×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
60	C₁₉×C₂²⋊Q₈	C₂³	1	2	yes	—
61	C₁₉×#121	—	2	2	no	—
62	C₁₉×#121	—	2	2	no	—
63	C₁₉×#121	—	2	1	no	—
64	C₁₉×#121	—	2	4	no	—
65	C₁₉×#121	C₂×C₄	1	4	yes	—
66	C₁₉×#121	C₂³	1	2	yes	—
67	C₁₉×#120	—	2	4	no	—
68	C₄×Q₈×C₁₉	—	2	2	no	—
69	C₄×Q₈×C₁₉	—	2	1	no	—
70	C₄×Q₈×C₁₉	C₂×C₄	1	2	yes	—
71	C₄×D₄×C₁₉	—	2	4	no	—
72	C₄×D₄×C₁₉	—	2	4	no	—
73	C₄×D₄×C₁₉	—	2	2	no	—
74	C₄×D₄×C₁₉	—	2	1	no	—
75	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
76	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
77	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
78	C₄×D₄×C₁₉	D₄	1	2	yes	—
79	C₄×D₄×C₁₉	D₄	1	2	yes	—
80	C₁₉×#117	—	2	1	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	C₂×C₄	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
90	C₂×C₄²×C₁₉	—	2	1	no	—
91	C₂×C₄²×C₁₉	—	2	2	no	—
92	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
93	C₁₉×C₄⋊C₈	—	2	1	no	—
94	C₁₉×C₄⋊C₈	—	2	1	no	—
95	C₁₉×C₂²⋊C₈	—	2	4	no	—
96	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
97	C₁₉×C₂²⋊C₈	C₂³	1	2	yes	—
98	C₄×C₈×C₁₉	—	2	1	no	—
99	C₄×C₈×C₁₉	—	2	1	no	—
100	C₁₉×#95	—	2	2	no	—
101	C₁₉×#95	—	2	1	no	—
102	C₁₉×#95	C₂³	1	1	yes	characteristic
103	C₁₉×#95	C₂³	1	2	yes	—
104	C₁₉×#95	C₂³	1	1	yes	characteristic
105	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
106	#41×C₁₉	—	4	2	no	—
107	#41×C₁₉	—	4	2	no	—
108	#41×C₁₉	—	8	4	no	—
109	C₂×Q₈×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	4	no	—
114	C₂×D₄×C₁₉	—	2	4	no	—
115	C₂×D₄×C₁₉	—	2	1	no	—
116	C₂×D₄×C₁₉	—	2	1	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
120	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
121	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	4	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	8	2	no	—
128	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	8	4	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	4	2	no	—
145	C₄⋊C₄×C₁₉	—	4	2	no	—
146	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
147	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
148	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
149	C₄⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	2	4	no	—
152	C₂²⋊C₄×C₁₉	—	2	2	no	—
153	C₂²⋊C₄×C₁₉	—	2	4	no	—
154	C₂²⋊C₄×C₁₉	—	2	2	no	—
155	C₂²⋊C₄×C₁₉	—	2	2	no	—
156	C₂²⋊C₄×C₁₉	—	4	4	no	—
157	C₂²⋊C₄×C₁₉	—	8	2	no	—
158	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
159	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
160	C₄²×C₁₉	—	2	4	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	4	2	no	—
163	C₄²×C₁₉	—	8	2	no	—
164	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
165	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
168	#17617	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂³×C₁₉	—	2	2	no	—
170	C₂³×C₁₉	—	2	2	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
175	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₁₉	—	4	2	no	—
177	Q₈×C₁₉	—	4	2	no	—
178	Q₈×C₁₉	—	8	1	no	—
179	D₄×C₁₉	—	2	4	no	—
180	D₄×C₁₉	—	2	4	no	—
181	D₄×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	4	2	no	—
184	D₄×C₁₉	—	4	2	no	—
185	D₄×C₁₉	—	8	1	no	—
186	D₄×C₁₉	—	8	4	no	—
187	D₄×C₁₉	—	8	4	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	4	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	8	4	no	—
207	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
208	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	#135	1	2	yes	—
213	C₂×C₄×C₁₉	#135	1	2	yes	—
214	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
216	C₈×C₁₉	—	4	2	no	—
217	C₈×C₁₉	—	4	2	no	—
218	#3506	C₂×C₁₉	1	1	yes	characteristic
219	#2972	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#2357	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1518	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#1517	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1516	C₂×C₁₉	1	4	yes	complemented
224	#1503	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#1502	C₂×C₁₉	1	1	yes	characteristic, complemented
226	#1501	C₂×C₁₉	1	4	yes	complemented
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	4	no	—
230	C₂²×C₁₉	—	2	4	no	—
231	C₂²×C₁₉	—	2	4	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	4	2	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	—	8	2	no	—
236	C₂²×C₁₉	—	8	2	no	—
237	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
239	C₂²×C₁₉	C₂×#135	1	1	yes	characteristic
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	2	1	no	—
242	C₄×C₁₉	—	2	4	no	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	2	1	no	—
245	C₄×C₁₉	—	4	2	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	4	2	no	—
248	C₄×C₁₉	—	4	2	no	—
249	C₄×C₁₉	—	8	1	no	—
250	C₄×C₁₉	—	8	2	no	—
251	C₄×C₁₉	#416	1	2	yes	—
252	C₄×C₁₉	#416	1	2	yes	—
253	#559	—	2	2	no	—
254	#556	C₄×C₁₉	1	2	yes	complemented
255	#555	C₄×C₁₉	1	2	yes	complemented
256	#553	—	2	2	no	—
257	#550	C₄×C₁₉	1	2	yes	complemented
258	#547	C₄×C₁₉	1	2	yes	complemented
259	#538	—	2	2	no	—
260	#535	—	2	1	no	—
261	#533	C₂²×C₁₉	1	1	yes	characteristic
262	#532	C₂²×C₁₉	1	1	yes	characteristic
263	#525	C₂²×C₁₉	1	4	yes	—
264	#520	—	2	1	no	—
265	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
266	C₈×D₄	—	2	2	no	—
267	C₈×D₄	—	2	2	no	—
268	#431	C₂²×C₁₉	1	1	yes	characteristic
269	#431	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
271	#390	—	2	1	no	—
272	#388	—	2	2	no	—
273	#382	C₂²×C₁₉	1	1	yes	characteristic
274	#381	C₂²×C₁₉	1	2	yes	—
275	C₄×C₄⋊C₄	—	2	1	no	—
276	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
277	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
278	#328	C₂²×C₁₉	1	2	yes	—
279	#328	C₂²×C₁₉	1	4	yes	—
280	#328	C₂²×C₁₉	1	2	yes	—
281	#327	C₂²×C₁₉	1	2	yes	—
282	#327	C₂²×C₁₉	1	4	yes	—
283	#327	C₂²×C₁₉	1	2	yes	—
284	C₂×C₁₉	—	2	1	no	—
285	C₂×C₁₉	—	2	1	no	—
286	C₂×C₁₉	—	4	4	no	—
287	C₂×C₁₉	—	8	2	no	—
288	C₂×C₁₉	#2883	1	1	yes	characteristic
289	C₂×C₁₉	C₂×#416	1	1	yes	characteristic
290	C₂×C₁₉	#2901	1	1	yes	characteristic
291	C₂×#41	—	2	1	no	—
292	C₂×#41	C₂×C₄×C₁₉	1	4	yes	—
293	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
295	C₂²×C₈	—	2	4	no	—
296	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
297	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
298	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
299	#127	—	2	2	no	—
300	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
301	#126	—	2	4	no	—
302	#125	—	2	1	no	—
303	#124	—	2	2	no	—
304	#124	—	2	4	no	—
305	#124	—	2	1	no	—
306	#123	—	2	4	no	—
307	#123	—	2	4	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	C₂×C₄×C₁₉	1	4	yes	—
310	C₂²⋊Q₈	C₂³×C₁₉	1	2	yes	—
311	#121	—	2	2	no	—
312	#121	—	2	2	no	—
313	#121	—	2	1	no	—
314	#121	—	2	4	no	—
315	#121	C₂×C₄×C₁₉	1	4	yes	—
316	#121	C₂³×C₁₉	1	2	yes	—
317	#120	—	2	4	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	C₂×C₄×C₁₉	1	2	yes	—
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
326	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
327	C₄×D₄	C₂×C₄×C₁₉	1	2	yes	—
328	C₄×D₄	D₄×C₁₉	1	2	yes	—
329	C₄×D₄	D₄×C₁₉	1	2	yes	—
330	#117	—	2	1	no	—
331	#117	—	2	2	no	—
332	#117	C₂×C₄×C₁₉	1	4	yes	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	2	1	no	—
345	C₂²⋊C₈	—	2	4	no	—
346	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
347	C₂²⋊C₈	C₂³×C₁₉	1	2	yes	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	#95	—	2	2	no	—
351	#95	—	2	1	no	—
352	#95	C₂³×C₁₉	1	1	yes	characteristic
353	#95	C₂³×C₁₉	1	2	yes	—
354	#95	C₂³×C₁₉	1	1	yes	characteristic
355	C₁₉	#17617	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
357	#41	—	4	2	no	—
358	#41	—	4	2	no	—
359	#41	—	8	4	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
371	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
372	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	8	2	no	—
379	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
383	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	8	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
398	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
399	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
400	C₄⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	8	2	no	—
409	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
410	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	4	2	no	—
414	C₄²	—	8	2	no	—
415	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
416	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
417	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
425	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
426	Q₈	—	4	2	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	8	1	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	8	1	no	—
436	D₄	—	8	4	no	—
437	D₄	—	8	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	8	4	no	—
457	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
458	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
459	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
460	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
461	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
462	C₂×C₄	C₁₉×#135	1	2	yes	—
463	C₂×C₄	C₁₉×#135	1	2	yes	—
464	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
479	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
480	C₂²	C₂×C₁₉×#135	1	1	yes	characteristic
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	4	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	2	no	—
492	C₄	C₁₉×#416	1	2	yes	—
493	C₄	C₁₉×#416	1	2	yes	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	4	4	no	—
497	C₂	—	8	2	no	—
498	C₂	C₁₉×#2883	1	1	yes	characteristic
499	C₂	C₂×C₁₉×#416	1	1	yes	characteristic
500	C₂	C₁₉×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3506	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2972	C₂	semidirect
3. C₁₉×#2357	C₂	semidirect
4. C₁₉×#1518	C₂	semidirect
5. C₁₉×#1517	C₂	semidirect
6. C₁₉×#1516	C₂	semidirect
7. C₁₉×#1503	C₂	semidirect
8. C₁₉×#1502	C₂	semidirect
9. C₁₉×#1501	C₂	semidirect
11. C₁₉×#556	C₄	semidirect
12. C₁₉×#555	C₄	semidirect
14. C₁₉×#550	C₄	semidirect
15. C₁₉×#547	C₄	semidirect
168. #17617	C₁₉	direct (N × H)
219. #2972	C₂×C₁₉	semidirect
220. #2357	C₂×C₁₉	semidirect
221. #1518	C₂×C₁₉	semidirect
222. #1517	C₂×C₁₉	semidirect
223. #1516	C₂×C₁₉	semidirect
224. #1503	C₂×C₁₉	semidirect
225. #1502	C₂×C₁₉	semidirect
226. #1501	C₂×C₁₉	semidirect
254. #556	C₄×C₁₉	semidirect
255. #555	C₄×C₁₉	semidirect
257. #550	C₄×C₁₉	semidirect
258. #547	C₄×C₁₉	semidirect
355. C₁₉	#17617	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×#3506	2
C₁₉×#2972	2
C₁₉×#2357	2
C₁₉×#1518	2
C₁₉×#1517	2
C₁₉×#1516	2
C₁₉×#1503	2
C₁₉×#1502	2
C₁₉×#1501	2
#17617	19

Subgroups — C19×#17617 #18023576

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#17617 #18023576