Subgroups — C₁₉×#33680 #18039639

Order 4864.

534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3177	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2951	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2235	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2229	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2228	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2209	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2208	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2189	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#2189	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#2176	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2175	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₉×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₉×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#2164	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
17	C₁₉×#541	—	2	1	no	—
18	C₁₉×#520	—	2	1	no	—
19	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
23	C₁₉×#499	C₂²	1	1	yes	characteristic
24	C₁₉×#494	C₂²	1	1	yes	characteristic
25	C₁₉×#491	—	2	1	no	—
26	C₁₉×#470	—	2	1	no	—
27	C₁₉×#467	C₂²	1	1	yes	characteristic
28	C₁₉×#467	C₂²	1	1	yes	characteristic
29	C₁₉×#441	—	2	1	no	—
30	C₁₉×#440	—	2	1	no	—
31	C₁₉×#440	—	2	1	no	—
32	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
33	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
34	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
35	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
36	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
37	C₄×D₈×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
39	C₁₉×#417	—	2	1	no	—
40	C₁₉×#405	C₂²	1	1	yes	characteristic
41	C₁₉×#367	C₂²	1	1	yes	characteristic
42	C₁₉×#367	C₂²	1	1	yes	characteristic
43	C₁₉×#366	C₂²	1	1	yes	characteristic
44	C₁₉×#366	C₂²	1	1	yes	characteristic
45	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
46	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
47	C₁₉×#358	C₂²	1	1	yes	characteristic
48	C₁₉×#358	C₂²	1	1	yes	characteristic
49	C₁₉×#358	C₂²	1	1	yes	characteristic
50	C₁₉×#358	C₂²	1	1	yes	characteristic
51	C₁₉×#358	C₂²	1	1	yes	characteristic
52	C₁₉×#358	C₂²	1	1	yes	characteristic
53	C₁₉×#357	C₂²	1	1	yes	characteristic
54	C₁₉×#357	C₂²	1	1	yes	characteristic
55	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₉×#346	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₁₉×#135	—	2	2	no	—
61	C₁₉×#135	—	2	2	no	—
62	C₂×Q₁₆×C₁₉	—	2	1	no	—
63	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×SD₁₆×C₁₉	—	2	1	no	—
67	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×#126	—	4	1	no	—
72	C₁₉×#126	—	4	1	no	—
73	C₁₉×#125	—	2	1	no	—
74	C₁₉×#125	—	4	1	no	—
75	C₁₉×#125	—	4	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	2	1	no	—
78	C₄×Q₈×C₁₉	—	2	1	no	—
79	C₄×Q₈×C₁₉	—	2	1	no	—
80	C₄×Q₈×C₁₉	—	2	1	no	—
81	C₄×Q₈×C₁₉	—	2	1	no	—
82	C₄×D₄×C₁₉	—	2	1	no	—
83	C₄×D₄×C₁₉	—	2	1	no	—
84	C₄×D₄×C₁₉	—	4	1	no	—
85	C₄×D₄×C₁₉	—	4	1	no	—
86	C₁₉×#117	—	4	1	no	—
87	C₁₉×#117	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₉	—	4	1	no	—
90	C₁₉×Q₃₂	—	2	2	no	—
91	C₁₉×Q₃₂	—	2	2	no	—
92	C₁₉×SD₃₂	—	2	2	no	—
93	C₁₉×SD₃₂	—	2	2	no	—
94	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
95	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
97	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
98	C₁₉×#107	—	2	1	no	—
99	C₁₉×#107	C₂³	1	1	yes	characteristic
100	C₁₉×#107	C₂³	1	1	yes	characteristic
101	C₁₉×#107	C₂³	1	1	yes	characteristic
102	C₁₉×#107	C₂³	1	1	yes	characteristic
103	C₁₉×#106	—	2	1	no	—
104	C₁₉×#103	—	2	1	no	—
105	C₁₉×#103	—	2	1	no	—
106	C₁₉×#103	—	2	1	no	—
107	C₁₉×#103	—	2	1	no	—
108	C₁₉×#103	—	2	1	no	—
109	C₁₉×#103	—	2	1	no	—
110	C₁₉×#102	—	2	1	no	—
111	C₁₉×#102	—	2	1	no	—
112	C₁₉×#97	D₄	1	1	yes	characteristic
113	C₁₉×#97	D₄	1	1	yes	characteristic
114	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
115	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
116	#41×C₁₉	—	2	4	no	—
117	#41×C₁₉	—	4	2	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	—	2	1	no	—
122	C₂×D₄×C₁₉	—	4	1	no	—
123	C₂²×C₄×C₁₉	—	4	1	no	—
124	C₂²×C₄×C₁₉	—	4	1	no	—
125	C₂²×C₄×C₁₉	—	4	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
128	Q₁₆×C₁₉	—	2	1	no	—
129	Q₁₆×C₁₉	—	2	1	no	—
130	Q₁₆×C₁₉	—	2	1	no	—
131	Q₁₆×C₁₉	—	2	1	no	—
132	Q₁₆×C₁₉	—	2	1	no	—
133	Q₁₆×C₁₉	—	4	2	no	—
134	Q₁₆×C₁₉	#41	1	2	yes	—
135	SD₁₆×C₁₉	—	2	4	no	—
136	D₈×C₁₉	—	2	1	no	—
137	D₈×C₁₉	#41	1	2	yes	—
138	M₁₆×C₁₉	—	4	1	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	1	no	—
149	C₄⋊C₄×C₁₉	—	4	1	no	—
150	C₄⋊C₄×C₁₉	—	4	1	no	—
151	C₄⋊C₄×C₁₉	—	4	1	no	—
152	C₄⋊C₄×C₁₉	—	4	1	no	—
153	C₄⋊C₄×C₁₉	—	4	1	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	—	4	1	no	—
157	C₄⋊C₄×C₁₉	—	4	1	no	—
158	C₄⋊C₄×C₁₉	—	4	1	no	—
159	C₄⋊C₄×C₁₉	—	4	1	no	—
160	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
161	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
162	C₂²⋊C₄×C₁₉	—	4	1	no	—
163	C₂²⋊C₄×C₁₉	—	4	1	no	—
164	C₂²⋊C₄×C₁₉	—	4	1	no	—
165	C₂²⋊C₄×C₁₉	—	4	1	no	—
166	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
167	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
168	C₄²×C₁₉	—	4	1	no	—
169	C₄²×C₁₉	—	4	1	no	—
170	C₄²×C₁₉	—	4	1	no	—
171	C₄²×C₁₉	—	4	1	no	—
172	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₁₆×C₁₉	—	2	1	no	—
175	C₁₆×C₁₉	—	2	1	no	—
176	C₁₆×C₁₉	—	2	1	no	—
177	C₁₆×C₁₉	—	2	1	no	—
178	#33680	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₁₉	—	4	1	no	—
180	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
181	Q₈×C₁₉	—	2	2	no	—
182	Q₈×C₁₉	—	4	1	no	—
183	Q₈×C₁₉	—	4	1	no	—
184	Q₈×C₁₉	—	4	1	no	—
185	Q₈×C₁₉	—	4	1	no	—
186	Q₈×C₁₉	—	4	1	no	—
187	D₄×C₁₉	—	2	2	no	—
188	D₄×C₁₉	—	4	4	no	—
189	D₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	—	4	1	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	4	1	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	16	1	no	—
201	C₂×C₄×C₁₉	—	16	1	no	—
202	C₂×C₄×C₁₉	—	16	1	no	—
203	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
206	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
207	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
209	C₈×C₁₉	—	2	1	no	—
210	C₈×C₁₉	—	2	1	no	—
211	C₈×C₁₉	—	2	1	no	—
212	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
213	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
214	#3177	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#2951	C₂×C₁₉	1	1	yes	characteristic
216	#2236	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#2235	C₂×C₁₉	1	1	yes	characteristic, complemented
218	#2229	C₂×C₁₉	1	1	yes	characteristic, complemented
219	#2228	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#2209	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#2208	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#2189	C₂×C₁₉	1	1	yes	characteristic
223	#2189	C₂×C₁₉	1	1	yes	characteristic
224	#2176	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#2175	C₂×C₁₉	1	1	yes	characteristic, complemented
226	C₄×Q₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
227	C₄×SD₃₂	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#2164	C₂×C₁₉	1	1	yes	characteristic, complemented
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	4	2	no	—
233	C₂²×C₁₉	—	8	1	no	—
234	C₂²×C₁₉	—	8	1	no	—
235	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
236	C₄×C₁₉	—	2	1	no	—
237	C₄×C₁₉	—	2	1	no	—
238	C₄×C₁₉	—	2	1	no	—
239	C₄×C₁₉	—	2	1	no	—
240	C₄×C₁₉	—	2	1	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	8	1	no	—
243	C₄×C₁₉	—	8	1	no	—
244	C₄×C₁₉	—	8	1	no	—
245	C₄×C₁₉	—	8	1	no	—
246	C₄×C₁₉	—	8	1	no	—
247	C₄×C₁₉	—	8	1	no	—
248	C₄×C₁₉	#525	1	1	yes	characteristic
249	C₄×C₁₉	#575	1	1	yes	characteristic
250	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
251	#541	—	2	1	no	—
252	#520	—	2	1	no	—
253	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
257	#499	C₂²×C₁₉	1	1	yes	characteristic
258	#494	C₂²×C₁₉	1	1	yes	characteristic
259	#491	—	2	1	no	—
260	#470	—	2	1	no	—
261	#467	C₂²×C₁₉	1	1	yes	characteristic
262	#467	C₂²×C₁₉	1	1	yes	characteristic
263	#441	—	2	1	no	—
264	#440	—	2	1	no	—
265	#440	—	2	1	no	—
266	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
267	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
268	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
269	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
270	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
271	C₄×D₈	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
273	#417	—	2	1	no	—
274	#405	C₂²×C₁₉	1	1	yes	characteristic
275	#367	C₂²×C₁₉	1	1	yes	characteristic
276	#367	C₂²×C₁₉	1	1	yes	characteristic
277	#366	C₂²×C₁₉	1	1	yes	characteristic
278	#366	C₂²×C₁₉	1	1	yes	characteristic
279	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
280	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
281	#358	C₂²×C₁₉	1	1	yes	characteristic
282	#358	C₂²×C₁₉	1	1	yes	characteristic
283	#358	C₂²×C₁₉	1	1	yes	characteristic
284	#358	C₂²×C₁₉	1	1	yes	characteristic
285	#358	C₂²×C₁₉	1	1	yes	characteristic
286	#358	C₂²×C₁₉	1	1	yes	characteristic
287	#357	C₂²×C₁₉	1	1	yes	characteristic
288	#357	C₂²×C₁₉	1	1	yes	characteristic
289	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
290	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
291	#346	C₂²×C₁₉	1	1	yes	characteristic
292	C₄×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
293	C₂×C₁₉	—	4	1	no	—
294	C₂×C₁₉	—	8	2	no	—
295	C₂×C₁₉	#3100	1	1	yes	characteristic
296	C₂×C₁₉	#3416	1	1	yes	characteristic
297	C₂×C₁₉	#3417	1	1	yes	characteristic
298	C₂×#41	—	2	1	no	—
299	#135	—	2	2	no	—
300	#135	—	2	2	no	—
301	C₂×Q₁₆	—	2	1	no	—
302	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
303	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
304	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×SD₁₆	—	2	1	no	—
306	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
309	C₄⋊Q₈	—	2	1	no	—
310	#126	—	4	1	no	—
311	#126	—	4	1	no	—
312	#125	—	2	1	no	—
313	#125	—	4	1	no	—
314	#125	—	4	1	no	—
315	C₂²⋊Q₈	—	2	1	no	—
316	C₂²⋊Q₈	—	2	1	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	4	1	no	—
324	C₄×D₄	—	4	1	no	—
325	#117	—	4	1	no	—
326	#117	D₄×C₁₉	1	1	yes	characteristic
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	4	1	no	—
329	Q₃₂	—	2	2	no	—
330	Q₃₂	—	2	2	no	—
331	SD₃₂	—	2	2	no	—
332	SD₃₂	—	2	2	no	—
333	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
334	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
335	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
336	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
337	#107	—	2	1	no	—
338	#107	C₂³×C₁₉	1	1	yes	characteristic
339	#107	C₂³×C₁₉	1	1	yes	characteristic
340	#107	C₂³×C₁₉	1	1	yes	characteristic
341	#107	C₂³×C₁₉	1	1	yes	characteristic
342	#106	—	2	1	no	—
343	#103	—	2	1	no	—
344	#103	—	2	1	no	—
345	#103	—	2	1	no	—
346	#103	—	2	1	no	—
347	#103	—	2	1	no	—
348	#103	—	2	1	no	—
349	#102	—	2	1	no	—
350	#102	—	2	1	no	—
351	#97	D₄×C₁₉	1	1	yes	characteristic
352	#97	D₄×C₁₉	1	1	yes	characteristic
353	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
354	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
355	C₁₉	#33680	1	1	yes	characteristic, direct product factor, Sylow
356	#41	—	2	4	no	—
357	#41	—	4	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂²×C₄	—	4	1	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	—	4	1	no	—
366	C₂²×C₄	—	4	1	no	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
368	Q₁₆	—	2	1	no	—
369	Q₁₆	—	2	1	no	—
370	Q₁₆	—	2	1	no	—
371	Q₁₆	—	2	1	no	—
372	Q₁₆	—	2	1	no	—
373	Q₁₆	—	4	2	no	—
374	Q₁₆	#41×C₁₉	1	2	yes	—
375	SD₁₆	—	2	4	no	—
376	D₈	—	2	1	no	—
377	D₈	#41×C₁₉	1	2	yes	—
378	M₁₆	—	4	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
383	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	—	4	1	no	—
392	C₄⋊C₄	—	4	1	no	—
393	C₄⋊C₄	—	4	1	no	—
394	C₄⋊C₄	—	4	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	—	4	1	no	—
400	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
401	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
402	C₂²⋊C₄	—	4	1	no	—
403	C₂²⋊C₄	—	4	1	no	—
404	C₂²⋊C₄	—	4	1	no	—
405	C₂²⋊C₄	—	4	1	no	—
406	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
407	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
408	C₄²	—	4	1	no	—
409	C₄²	—	4	1	no	—
410	C₄²	—	4	1	no	—
411	C₄²	—	4	1	no	—
412	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₁₆	—	2	1	no	—
415	C₁₆	—	2	1	no	—
416	C₁₆	—	2	1	no	—
417	C₁₆	—	2	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
420	Q₈	—	2	2	no	—
421	Q₈	—	4	1	no	—
422	Q₈	—	4	1	no	—
423	Q₈	—	4	1	no	—
424	Q₈	—	4	1	no	—
425	Q₈	—	4	1	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	16	1	no	—
440	C₂×C₄	—	16	1	no	—
441	C₂×C₄	—	16	1	no	—
442	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
443	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
444	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
445	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
446	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	2	1	no	—
451	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
452	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	2	no	—
466	C₄	—	8	1	no	—
467	C₄	—	8	1	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	1	no	—
472	C₄	C₁₉×#525	1	1	yes	characteristic
473	C₄	C₁₉×#575	1	1	yes	characteristic
474	C₂	—	4	1	no	—
475	C₂	—	8	2	no	—
476	C₂	C₁₉×#3100	1	1	yes	characteristic
477	C₂	C₁₉×#3416	1	1	yes	characteristic
478	C₂	C₁₉×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#117 ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3177	C₂	semidirect
3. C₁₉×#2236	C₂	semidirect
4. C₁₉×#2235	C₂	semidirect
5. C₁₉×#2229	C₂	semidirect
6. C₁₉×#2228	C₂	semidirect
7. C₁₉×#2209	C₂	semidirect
8. C₁₉×#2208	C₂	semidirect
11. C₁₉×#2176	C₂	semidirect
12. C₁₉×#2175	C₂	semidirect
13. C₄×C₁₉×Q₃₂	C₂	semidirect
14. C₄×C₁₉×SD₃₂	C₂	semidirect
15. C₁₉×#2164	C₂	semidirect
178. #33680	C₁₉	direct (N × H)
214. #3177	C₂×C₁₉	semidirect
216. #2236	C₂×C₁₉	semidirect
217. #2235	C₂×C₁₉	semidirect
218. #2229	C₂×C₁₉	semidirect
219. #2228	C₂×C₁₉	semidirect
220. #2209	C₂×C₁₉	semidirect
221. #2208	C₂×C₁₉	semidirect
224. #2176	C₂×C₁₉	semidirect
225. #2175	C₂×C₁₉	semidirect
226. C₄×Q₃₂	C₂×C₁₉	semidirect
227. C₄×SD₃₂	C₂×C₁₉	semidirect
228. #2164	C₂×C₁₉	semidirect
355. C₁₉	#33680	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×#3177	2
C₁₉×#2951	2
C₁₉×#2236	2
C₁₉×#2235	2
C₁₉×#2229	2
C₁₉×#2228	2
C₁₉×#2209	2
C₁₉×#2208	2
C₁₉×#2189	2
C₁₉×#2176	2
C₁₉×#2175	2
C₄×C₁₉×Q₃₂	2
C₄×C₁₉×SD₃₂	2
C₁₉×#2164	2
#33680	19

Subgroups — C19×#33680 #18039639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33680 #18039639