Subgroups — C₁₉×#33883 #18039842

Order 4864.

548 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3338	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3285	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2243	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2235	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2233	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2225	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2219	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2217	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#2211	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#2188	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#2176	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#2168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₉×#2139	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×#358	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#135	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
18	C₁₉×#554	—	2	1	no	—
19	C₁₉×#548	—	2	1	no	—
20	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×Q₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₉×SD₃₂	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
24	C₂²×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#500	C₂²	1	1	yes	characteristic
26	C₁₉×#495	C₂²	1	1	yes	characteristic
27	C₁₉×#484	—	2	1	no	—
28	C₁₉×#484	—	2	1	no	—
29	C₁₉×#477	—	2	1	no	—
30	C₁₉×#467	C₂²	1	1	yes	characteristic
31	C₁₉×#467	C₂²	1	1	yes	characteristic
32	C₁₉×#467	C₂²	1	1	yes	characteristic
33	C₁₉×#466	C₂²	1	1	yes	characteristic
34	C₁₉×#464	—	2	1	no	—
35	C₁₉×#452	—	2	1	no	—
36	C₁₉×#448	—	2	1	no	—
37	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
38	C₄×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₁₉	C₂²	1	1	yes	characteristic
40	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
42	C₁₉×#367	C₂²	1	1	yes	characteristic
43	C₁₉×#367	C₂²	1	1	yes	characteristic
44	C₁₉×#367	C₂²	1	1	yes	characteristic
45	C₁₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
46	C₁₉×#358	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×#357	C₂²	1	1	yes	characteristic
56	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₁₉×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
58	C₁₉×#346	C₂²	1	1	yes	characteristic
59	C₂×#41×C₁₉	—	2	1	no	—
60	C₂²×Q₈×C₁₉	—	2	1	no	—
61	C₁₉×#135	—	2	2	no	—
62	C₁₉×#135	—	4	1	no	—
63	C₂×Q₁₆×C₁₉	—	2	2	no	—
64	C₂×Q₁₆×C₁₉	—	2	1	no	—
65	C₂×Q₁₆×C₁₉	—	4	1	no	—
66	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×Q₁₆×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×SD₁₆×C₁₉	—	2	1	no	—
70	C₂×SD₁₆×C₁₉	—	2	1	no	—
71	C₂×D₈×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
74	C₁₉×C₄⋊Q₈	—	2	1	no	—
75	C₁₉×#125	—	4	1	no	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#124	—	4	1	no	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	1	no	—
81	C₁₉×C₂²⋊Q₈	—	4	1	no	—
82	C₁₉×C₂²⋊Q₈	—	4	1	no	—
83	C₁₉×C₂²⋊Q₈	—	4	1	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#121	—	4	1	no	—
86	C₄×Q₈×C₁₉	—	2	1	no	—
87	C₄×Q₈×C₁₉	—	2	1	no	—
88	C₄×D₄×C₁₉	—	4	1	no	—
89	C₄×D₄×C₁₉	—	4	1	no	—
90	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₁₉×Q₃₂	—	2	2	no	—
94	C₁₉×Q₃₂	—	4	1	no	—
95	C₁₉×SD₃₂	—	4	1	no	—
96	C₁₉×M₃₂	—	4	1	no	—
97	C₂×C₁₆×C₁₉	—	4	1	no	—
98	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
99	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
100	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
101	C₂×C₁₆×C₁₉	C₂³	1	1	yes	characteristic
102	C₁₉×#107	—	2	1	no	—
103	C₁₉×#107	—	2	1	no	—
104	C₁₉×#107	—	2	1	no	—
105	C₁₉×#107	C₂³	1	1	yes	characteristic
106	C₁₉×#107	C₂³	1	1	yes	characteristic
107	C₁₉×#107	C₂³	1	1	yes	characteristic
108	C₁₉×#107	C₂³	1	1	yes	characteristic
109	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
110	C₁₉×#103	—	2	1	no	—
111	C₁₉×#103	—	2	1	no	—
112	C₁₉×#103	—	2	1	no	—
113	C₁₉×#103	—	2	1	no	—
114	C₁₉×#103	—	2	1	no	—
115	C₁₉×#102	—	2	1	no	—
116	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
117	C₁₉×C₂²⋊C₈	D₄	1	1	yes	characteristic
118	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
119	#41×C₁₉	—	4	2	no	—
120	#41×C₁₉	—	8	1	no	—
121	C₂×Q₈×C₁₉	—	2	1	no	—
122	C₂×Q₈×C₁₉	—	2	1	no	—
123	C₂×Q₈×C₁₉	—	2	1	no	—
124	C₂×Q₈×C₁₉	—	4	2	no	—
125	C₂×Q₈×C₁₉	—	4	1	no	—
126	C₂×Q₈×C₁₉	—	4	1	no	—
127	C₂×Q₈×C₁₉	—	8	1	no	—
128	C₂×D₄×C₁₉	—	2	1	no	—
129	C₂×D₄×C₁₉	—	4	1	no	—
130	C₂×D₄×C₁₉	—	4	1	no	—
131	C₂×D₄×C₁₉	D₈	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	—	4	1	no	—
133	C₂²×C₄×C₁₉	—	4	1	no	—
134	C₂²×C₄×C₁₉	—	4	1	no	—
135	C₂²×C₄×C₁₉	—	4	1	no	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	Q₁₆×C₁₉	—	2	1	no	—
139	Q₁₆×C₁₉	—	2	1	no	—
140	Q₁₆×C₁₉	—	2	1	no	—
141	Q₁₆×C₁₉	—	2	1	no	—
142	Q₁₆×C₁₉	—	2	1	no	—
143	Q₁₆×C₁₉	—	4	2	no	—
144	Q₁₆×C₁₉	#41	1	2	yes	—
145	SD₁₆×C₁₉	—	4	2	no	—
146	SD₁₆×C₁₉	—	8	1	no	—
147	D₈×C₁₉	—	2	1	no	—
148	D₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	—	2	1	no	—
151	C₂×C₈×C₁₉	—	2	1	no	—
152	C₂×C₈×C₁₉	—	2	1	no	—
153	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
157	C₄⋊C₄×C₁₉	—	2	1	no	—
158	C₄⋊C₄×C₁₉	—	2	1	no	—
159	C₄⋊C₄×C₁₉	—	2	1	no	—
160	C₄⋊C₄×C₁₉	—	2	1	no	—
161	C₄⋊C₄×C₁₉	—	4	1	no	—
162	C₄⋊C₄×C₁₉	—	4	1	no	—
163	C₄⋊C₄×C₁₉	—	4	1	no	—
164	C₄⋊C₄×C₁₉	—	4	1	no	—
165	C₄⋊C₄×C₁₉	—	4	1	no	—
166	C₄⋊C₄×C₁₉	—	4	1	no	—
167	C₄⋊C₄×C₁₉	—	4	1	no	—
168	C₄⋊C₄×C₁₉	—	4	1	no	—
169	C₄⋊C₄×C₁₉	D₈	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₉	—	4	1	no	—
171	C₂²⋊C₄×C₁₉	—	4	1	no	—
172	C₂²⋊C₄×C₁₉	—	4	1	no	—
173	C₂²⋊C₄×C₁₉	—	4	1	no	—
174	C₂²⋊C₄×C₁₉	—	4	1	no	—
175	C₂²⋊C₄×C₁₉	—	4	1	no	—
176	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
177	C₂²⋊C₄×C₁₉	D₈	1	1	yes	characteristic
178	C₄²×C₁₉	—	4	1	no	—
179	C₄²×C₁₉	—	4	1	no	—
180	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
181	C₁₆×C₁₉	—	2	1	no	—
182	C₁₆×C₁₉	—	2	1	no	—
183	C₁₆×C₁₉	—	2	1	no	—
184	C₁₆×C₁₉	—	2	1	no	—
185	#33883	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
188	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
189	Q₈×C₁₉	—	2	2	no	—
190	Q₈×C₁₉	—	4	1	no	—
191	Q₈×C₁₉	—	4	1	no	—
192	Q₈×C₁₉	—	4	1	no	—
193	Q₈×C₁₉	—	4	1	no	—
194	Q₈×C₁₉	—	4	1	no	—
195	Q₈×C₁₉	—	8	2	no	—
196	Q₈×C₁₉	—	16	1	no	—
197	D₄×C₁₉	—	2	2	no	—
198	D₄×C₁₉	—	4	1	no	—
199	D₄×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	8	2	no	—
201	D₄×C₁₉	—	8	2	no	—
202	C₂×C₄×C₁₉	—	2	1	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	1	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	1	no	—
213	C₂×C₄×C₁₉	—	8	2	no	—
214	C₂×C₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	—	16	1	no	—
216	C₂×C₄×C₁₉	—	16	1	no	—
217	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
219	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
220	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₈×C₁₉	—	2	1	no	—
223	C₈×C₁₉	—	2	1	no	—
224	C₈×C₁₉	—	2	1	no	—
225	C₈×C₁₉	C₂×#41	1	1	yes	characteristic
226	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
227	#3338	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#3285	C₂×C₁₉	1	1	yes	characteristic
229	#2243	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#2235	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#2233	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#2225	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2219	C₂×C₁₉	1	1	yes	characteristic, complemented
234	#2217	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#2211	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#2189	C₂×C₁₉	1	1	yes	characteristic, complemented
237	#2188	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#2176	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#2168	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#2139	C₂×C₁₉	1	1	yes	characteristic, complemented
241	C₂×#358	C₂×C₁₉	1	1	yes	characteristic, complemented
242	C₂²×C₁₉	—	2	1	no	—
243	C₂²×C₁₉	—	2	1	no	—
244	C₂²×C₁₉	—	2	1	no	—
245	C₂²×C₁₉	—	2	1	no	—
246	C₂²×C₁₉	—	2	1	no	—
247	C₂²×C₁₉	—	8	1	no	—
248	C₂²×C₁₉	—	8	1	no	—
249	C₂²×C₁₉	—	8	1	no	—
250	C₂²×C₁₉	#510	1	2	yes	—
251	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	2	1	no	—
255	C₄×C₁₉	—	2	1	no	—
256	C₄×C₁₉	—	4	2	no	—
257	C₄×C₁₉	—	8	1	no	—
258	C₄×C₁₉	—	8	1	no	—
259	C₄×C₁₉	—	8	1	no	—
260	C₄×C₁₉	—	8	1	no	—
261	C₄×C₁₉	—	8	1	no	—
262	C₄×C₁₉	—	8	1	no	—
263	C₄×C₁₉	#546	1	1	yes	characteristic
264	C₄×C₁₉	#577	1	1	yes	characteristic
265	C₂×#135	C₂²×C₁₉	1	1	yes	characteristic
266	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
267	#554	—	2	1	no	—
268	#548	—	2	1	no	—
269	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×Q₃₂	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×SD₃₂	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
273	C₂²×C₁₆	C₂²×C₁₉	1	1	yes	characteristic
274	#500	C₂²×C₁₉	1	1	yes	characteristic
275	#495	C₂²×C₁₉	1	1	yes	characteristic
276	#484	—	2	1	no	—
277	#484	—	2	1	no	—
278	#477	—	2	1	no	—
279	#467	C₂²×C₁₉	1	1	yes	characteristic
280	#467	C₂²×C₁₉	1	1	yes	characteristic
281	#467	C₂²×C₁₉	1	1	yes	characteristic
282	#466	C₂²×C₁₉	1	1	yes	characteristic
283	#464	—	2	1	no	—
284	#452	—	2	1	no	—
285	#448	—	2	1	no	—
286	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
287	C₄×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
288	C₈×D₄	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
290	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
291	#367	C₂²×C₁₉	1	1	yes	characteristic
292	#367	C₂²×C₁₉	1	1	yes	characteristic
293	#367	C₂²×C₁₉	1	1	yes	characteristic
294	C₄⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
295	#358	C₂²×C₁₉	1	1	yes	characteristic
296	#358	C₂²×C₁₉	1	1	yes	characteristic
297	#358	C₂²×C₁₉	1	1	yes	characteristic
298	#358	C₂²×C₁₉	1	1	yes	characteristic
299	#358	C₂²×C₁₉	1	1	yes	characteristic
300	#358	C₂²×C₁₉	1	1	yes	characteristic
301	#358	C₂²×C₁₉	1	1	yes	characteristic
302	#357	C₂²×C₁₉	1	1	yes	characteristic
303	#357	C₂²×C₁₉	1	1	yes	characteristic
304	#357	C₂²×C₁₉	1	1	yes	characteristic
305	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
306	C₂²⋊C₁₆	C₂²×C₁₉	1	1	yes	characteristic
307	#346	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×C₁₉	—	2	2	no	—
309	C₂×C₁₉	—	4	1	no	—
310	C₂×C₁₉	—	16	1	no	—
311	C₂×C₁₉	#3294	1	1	yes	characteristic
312	C₂×C₁₉	C₂×#510	1	1	yes	characteristic
313	C₂×C₁₉	#3416	1	1	yes	characteristic
314	C₂×#41	—	2	1	no	—
315	C₂²×Q₈	—	2	1	no	—
316	#135	—	2	2	no	—
317	#135	—	4	1	no	—
318	C₂×Q₁₆	—	2	2	no	—
319	C₂×Q₁₆	—	2	1	no	—
320	C₂×Q₁₆	—	4	1	no	—
321	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
322	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×Q₁₆	C₂³×C₁₉	1	1	yes	characteristic
324	C₂×SD₁₆	—	2	1	no	—
325	C₂×SD₁₆	—	2	1	no	—
326	C₂×D₈	C₂³×C₁₉	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
329	C₄⋊Q₈	—	2	1	no	—
330	#125	—	4	1	no	—
331	#124	—	2	1	no	—
332	#124	—	4	1	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	—	4	1	no	—
337	C₂²⋊Q₈	—	4	1	no	—
338	C₂²⋊Q₈	—	4	1	no	—
339	#121	—	2	1	no	—
340	#121	—	4	1	no	—
341	C₄×Q₈	—	2	1	no	—
342	C₄×Q₈	—	2	1	no	—
343	C₄×D₄	—	4	1	no	—
344	C₄×D₄	—	4	1	no	—
345	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	Q₃₂	—	2	2	no	—
349	Q₃₂	—	4	1	no	—
350	SD₃₂	—	4	1	no	—
351	M₃₂	—	4	1	no	—
352	C₂×C₁₆	—	4	1	no	—
353	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
354	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
355	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
356	C₂×C₁₆	C₂³×C₁₉	1	1	yes	characteristic
357	#107	—	2	1	no	—
358	#107	—	2	1	no	—
359	#107	—	2	1	no	—
360	#107	C₂³×C₁₉	1	1	yes	characteristic
361	#107	C₂³×C₁₉	1	1	yes	characteristic
362	#107	C₂³×C₁₉	1	1	yes	characteristic
363	#107	C₂³×C₁₉	1	1	yes	characteristic
364	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
365	#103	—	2	1	no	—
366	#103	—	2	1	no	—
367	#103	—	2	1	no	—
368	#103	—	2	1	no	—
369	#103	—	2	1	no	—
370	#102	—	2	1	no	—
371	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
372	C₂²⋊C₈	D₄×C₁₉	1	1	yes	characteristic
373	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
374	C₁₉	#33883	1	1	yes	characteristic, direct product factor, Sylow
375	#41	—	4	2	no	—
376	#41	—	8	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	4	2	no	—
381	C₂×Q₈	—	4	1	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂×Q₈	—	8	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	—	4	1	no	—
387	C₂×D₄	D₈×C₁₉	1	1	yes	characteristic
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
394	Q₁₆	—	2	1	no	—
395	Q₁₆	—	2	1	no	—
396	Q₁₆	—	2	1	no	—
397	Q₁₆	—	2	1	no	—
398	Q₁₆	—	2	1	no	—
399	Q₁₆	—	4	2	no	—
400	Q₁₆	#41×C₁₉	1	2	yes	—
401	SD₁₆	—	4	2	no	—
402	SD₁₆	—	8	1	no	—
403	D₈	—	2	1	no	—
404	D₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	4	1	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	4	1	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₄⋊C₄	D₈×C₁₉	1	1	yes	characteristic
426	C₂²⋊C₄	—	4	1	no	—
427	C₂²⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₂²⋊C₄	—	4	1	no	—
430	C₂²⋊C₄	—	4	1	no	—
431	C₂²⋊C₄	—	4	1	no	—
432	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
433	C₂²⋊C₄	D₈×C₁₉	1	1	yes	characteristic
434	C₄²	—	4	1	no	—
435	C₄²	—	4	1	no	—
436	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
437	C₁₆	—	2	1	no	—
438	C₁₆	—	2	1	no	—
439	C₁₆	—	2	1	no	—
440	C₁₆	—	2	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
443	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
444	Q₈	—	2	2	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	4	1	no	—
447	Q₈	—	4	1	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	1	no	—
450	Q₈	—	8	2	no	—
451	Q₈	—	16	1	no	—
452	D₄	—	2	2	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	8	2	no	—
456	D₄	—	8	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	8	2	no	—
469	C₂×C₄	—	8	2	no	—
470	C₂×C₄	—	16	1	no	—
471	C₂×C₄	—	16	1	no	—
472	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
474	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
475	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
477	C₈	—	2	1	no	—
478	C₈	—	2	1	no	—
479	C₈	—	2	1	no	—
480	C₈	C₂×#41×C₁₉	1	1	yes	characteristic
481	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	C₁₉×#510	1	2	yes	—
491	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	4	2	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	1	no	—
499	C₄	—	8	1	no	—
500	C₄	—	8	1	no	—
501	C₄	—	8	1	no	—
502	C₄	—	8	1	no	—
503	C₄	C₁₉×#546	1	1	yes	characteristic
504	C₄	C₁₉×#577	1	1	yes	characteristic
505	C₂	—	2	2	no	—
506	C₂	—	4	1	no	—
507	C₂	—	16	1	no	—
508	C₂	C₁₉×#3294	1	1	yes	characteristic
509	C₂	C₂×C₁₉×#510	1	1	yes	characteristic
510	C₂	C₁₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₁₉×#3285	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄×D₄×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3338	C₂	semidirect
3. C₁₉×#2243	C₂	semidirect
4. C₁₉×#2235	C₂	semidirect
5. C₁₉×#2233	C₂	semidirect
6. C₁₉×#2225	C₂	semidirect
7. C₁₉×#2219	C₂	semidirect
8. C₁₉×#2217	C₂	semidirect
9. C₁₉×#2211	C₂	semidirect
10. C₁₉×#2189	C₂	semidirect
11. C₁₉×#2188	C₂	semidirect
12. C₁₉×#2176	C₂	semidirect
13. C₁₉×#2168	C₂	semidirect
14. C₁₉×#2139	C₂	semidirect
15. C₂×C₁₉×#358	C₂	semidirect
185. #33883	C₁₉	direct (N × H)
227. #3338	C₂×C₁₉	semidirect
229. #2243	C₂×C₁₉	semidirect
230. #2235	C₂×C₁₉	semidirect
231. #2233	C₂×C₁₉	semidirect
232. #2225	C₂×C₁₉	semidirect
233. #2219	C₂×C₁₉	semidirect
234. #2217	C₂×C₁₉	semidirect
235. #2211	C₂×C₁₉	semidirect
236. #2189	C₂×C₁₉	semidirect
237. #2188	C₂×C₁₉	semidirect
238. #2176	C₂×C₁₉	semidirect
239. #2168	C₂×C₁₉	semidirect
240. #2139	C₂×C₁₉	semidirect
241. C₂×#358	C₂×C₁₉	semidirect
374. C₁₉	#33883	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×#3338	2
C₁₉×#3285	2
C₁₉×#2243	2
C₁₉×#2235	2
C₁₉×#2233	2
C₁₉×#2225	2
C₁₉×#2219	2
C₁₉×#2217	2
C₁₉×#2211	2
C₁₉×#2189	2
C₁₉×#2188	2
C₁₉×#2176	2
C₁₉×#2168	2
C₁₉×#2139	2
C₂×C₁₉×#358	2
#33883	19

Subgroups — C19×#33883 #18039842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33883 #18039842