Subgroups — C₁₉×#60453 #18066412

Order 4864.

2722 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3449	C₂	1	2	yes	maximal, complemented
4	C₁₉×#3063	C₂	1	8	yes	maximal, complemented
5	C₁₉×#3062	C₂	1	8	yes	maximal, complemented
6	C₁₉×#3054	C₂	1	4	yes	maximal, complemented
7	C₁₉×#3050	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2911	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#416	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₁₉	C₂²	1	2	yes	—
11	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
12	C₁₉×#575	—	2	8	no	—
13	C₂×C₁₉×#137	C₂²	1	4	yes	complemented
14	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
15	C₂×C₁₉×#135	C₂²	1	4	yes	—
16	C₂×C₁₉×#131	—	2	8	no	—
17	C₂×C₁₉×#131	C₂²	1	8	yes	complemented
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₁₉	C₂²	1	2	yes	complemented
22	C₁₉×#537	C₂²	1	8	yes	—
23	C₁₉×#536	—	2	2	no	—
24	C₁₉×#536	C₂²	1	4	yes	complemented
25	C₁₉×#535	—	2	2	no	—
26	C₁₉×#535	C₂²	1	4	yes	complemented
27	C₁₉×#534	—	2	4	no	—
28	C₁₉×#532	—	2	4	no	—
29	C₁₉×#525	—	2	4	no	—
30	C₁₉×#525	C₂²	1	8	yes	complemented
31	C₂×C₁₉×#117	C₂²	1	2	yes	—
32	C₁₉×#470	C₂²	1	8	yes	complemented
33	C₁₉×#469	C₂²	1	8	yes	complemented
34	C₁₉×#468	C₂²	1	16	yes	complemented
35	C₁₉×#467	C₂²	1	8	yes	complemented
36	C₁₉×#466	C₂²	1	8	yes	complemented
37	C₁₉×#465	C₂²	1	16	yes	complemented
38	C₁₉×#428	C₂²	1	8	yes	complemented
39	C₁₉×#427	C₂²	1	4	yes	complemented
40	C₁₉×#416	C₂²	1	4	yes	complemented
41	C₁₉×#416	C₂²	1	4	yes	complemented
42	C₁₉×#416	C₂²	1	8	yes	complemented
43	C₂×C₁₉×#103	C₂²	1	4	yes	complemented
44	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
45	C₂×#41×C₁₉	—	2	4	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	2	no	—
48	C₂×#41×C₁₉	—	2	4	no	—
49	C₂×#41×C₁₉	—	2	8	no	—
50	C₂×#41×C₁₉	—	2	8	no	—
51	C₂×#41×C₁₉	D₄	1	4	yes	—
52	C₂×#41×C₁₉	C₂³	1	4	yes	—
53	C₂×#41×C₁₉	C₂³	1	4	yes	—
54	C₂×#41×C₁₉	C₂³	1	4	yes	—
55	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₉	—	2	2	no	—
58	C₂²×D₄×C₁₉	D₄	1	2	yes	—
59	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₉	—	2	2	no	—
62	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₁₉×#137	—	2	16	no	—
65	C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
66	C₁₉×#135	—	2	16	no	—
67	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
68	C₂×SD₁₆×C₁₉	C₂³	1	8	yes	—
69	C₂×D₈×C₁₉	C₂³	1	4	yes	—
70	C₁₉×#131	—	2	32	no	—
71	C₂×M₁₆×C₁₉	—	2	8	no	—
72	C₂×M₁₆×C₁₉	D₄	1	8	yes	complemented
73	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
74	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
75	C₂²×C₈×C₁₉	—	2	4	no	—
76	C₂²×C₈×C₁₉	—	2	8	no	—
77	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
78	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	8	yes	—
81	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
82	C₁₉×C₄⋊Q₈	—	2	4	no	—
83	C₁₉×#127	—	2	4	no	—
84	C₁₉×#124	—	2	4	no	—
85	C₁₉×#124	—	2	4	no	—
86	C₁₉×#123	—	2	8	no	—
87	C₁₉×#123	—	2	8	no	—
88	C₁₉×C₂²⋊Q₈	—	2	8	no	—
89	C₁₉×C₂²⋊Q₈	C₂³	1	16	yes	—
90	C₁₉×#121	—	2	8	no	—
91	C₁₉×#121	—	2	16	no	—
92	C₁₉×#121	C₂³	1	16	yes	—
93	C₁₉×#120	—	2	8	no	—
94	C₁₉×#120	—	2	8	no	—
95	C₄×D₄×C₁₉	—	2	16	no	—
96	C₁₉×#117	—	2	2	no	—
97	C₁₉×#117	—	2	2	no	—
98	C₁₉×#117	C₂³	1	4	yes	—
99	C₁₉×#117	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₄²×C₁₉	—	2	2	no	—
103	C₁₉×#107	C₂³	1	8	yes	—
104	C₁₉×#106	C₂³	1	8	yes	—
105	C₁₉×#103	C₂³	1	8	yes	—
106	C₁₉×#103	C₂³	1	8	yes	—
107	C₁₉×#102	C₂³	1	8	yes	—
108	C₁₉×#102	C₂³	1	8	yes	—
109	C₂⁴×C₁₉	—	2	2	no	—
110	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
111	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
112	#41×C₁₉	—	2	16	no	—
113	#41×C₁₉	—	2	8	no	—
114	#41×C₁₉	—	2	8	no	—
115	#41×C₁₉	—	2	8	no	—
116	#41×C₁₉	—	2	8	no	—
117	#41×C₁₉	—	2	8	no	—
118	#41×C₁₉	—	2	8	no	—
119	#41×C₁₉	—	4	8	no	—
120	#41×C₁₉	—	4	8	no	—
121	C₂×Q₈×C₁₉	—	2	4	no	—
122	C₂×Q₈×C₁₉	—	2	2	no	—
123	C₂×Q₈×C₁₉	—	2	4	no	—
124	C₂×Q₈×C₁₉	—	2	4	no	—
125	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
126	C₂×Q₈×C₁₉	C₂⁴	1	4	yes	—
127	C₂×D₄×C₁₉	—	2	8	no	—
128	C₂×D₄×C₁₉	—	2	4	no	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	16	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	2	no	—
134	C₂×D₄×C₁₉	—	2	4	no	—
135	C₂×D₄×C₁₉	—	4	8	no	—
136	C₂×D₄×C₁₉	C₂×D₄	1	8	yes	—
137	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
138	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₉	—	2	4	no	—
140	C₂²×C₄×C₁₉	—	2	4	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	4	no	—
143	C₂²×C₄×C₁₉	—	2	4	no	—
144	C₂²×C₄×C₁₉	—	2	4	no	—
145	C₂²×C₄×C₁₉	—	4	8	no	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₉	#41	1	4	yes	—
152	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	Q₁₆×C₁₉	—	2	8	no	—
156	SD₁₆×C₁₉	—	2	16	no	—
157	D₈×C₁₉	—	2	8	no	—
158	M₁₆×C₁₉	—	2	16	no	—
159	M₁₆×C₁₉	C₂×D₄	1	16	yes	—
160	C₂×C₈×C₁₉	—	2	2	no	—
161	C₂×C₈×C₁₉	—	2	2	no	—
162	C₂×C₈×C₁₉	—	2	8	no	—
163	C₂×C₈×C₁₉	—	2	16	no	—
164	C₂×C₈×C₁₉	C₂×D₄	1	8	yes	—
165	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
166	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
167	C₂×C₈×C₁₉	C₂⁴	1	4	yes	—
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	—	2	16	no	—
170	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
171	C₂²⋊C₄×C₁₉	—	2	4	no	—
172	C₂²⋊C₄×C₁₉	—	2	4	no	—
173	C₂²⋊C₄×C₁₉	—	2	16	no	—
174	C₂²⋊C₄×C₁₉	—	2	16	no	—
175	C₄²×C₁₉	—	2	4	no	—
176	C₄²×C₁₉	—	2	4	no	—
177	#60453	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂³×C₁₉	—	2	4	no	—
179	C₂³×C₁₉	—	2	4	no	—
180	C₂³×C₁₉	—	4	2	no	—
181	C₂³×C₁₉	—	4	4	no	—
182	C₂³×C₁₉	—	4	4	no	—
183	C₂³×C₁₉	—	8	4	no	—
184	C₂³×C₁₉	#121	1	4	yes	—
185	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
186	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
188	Q₈×C₁₉	—	2	8	no	—
189	Q₈×C₁₉	—	2	4	no	—
190	Q₈×C₁₉	—	2	4	no	—
191	Q₈×C₁₉	—	4	4	no	—
192	D₄×C₁₉	—	2	16	no	—
193	D₄×C₁₉	—	2	8	no	—
194	D₄×C₁₉	—	2	4	no	—
195	D₄×C₁₉	—	2	4	no	—
196	D₄×C₁₉	—	4	8	no	—
197	D₄×C₁₉	—	4	8	no	—
198	D₄×C₁₉	—	4	4	no	—
199	D₄×C₁₉	—	8	16	no	—
200	C₂×C₄×C₁₉	—	2	4	no	—
201	C₂×C₄×C₁₉	—	2	8	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	4	no	—
204	C₂×C₄×C₁₉	—	2	8	no	—
205	C₂×C₄×C₁₉	—	2	4	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	4	8	no	—
208	C₂×C₄×C₁₉	—	4	8	no	—
209	C₂×C₄×C₁₉	—	8	4	no	—
210	C₂×C₄×C₁₉	#121	1	8	yes	—
211	C₂×C₄×C₁₉	#121	1	4	yes	—
212	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
218	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
219	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
220	C₈×C₁₉	—	2	2	no	—
221	C₈×C₁₉	—	2	2	no	—
222	C₈×C₁₉	C₂²×D₄	1	8	yes	—
223	C₂×#575	C₂×C₁₉	1	1	yes	characteristic, complemented
224	C₂²×#131	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#3449	C₂×C₁₉	1	2	yes	complemented
226	#3063	C₂×C₁₉	1	8	yes	complemented
227	#3062	C₂×C₁₉	1	8	yes	complemented
228	#3054	C₂×C₁₉	1	4	yes	complemented
229	#3050	C₂×C₁₉	1	4	yes	complemented
230	#2911	C₂×C₁₉	1	1	yes	characteristic, complemented
231	C₂×#416	C₂×C₁₉	1	2	yes	complemented
232	C₂²×C₁₉	—	2	4	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	8	no	—
235	C₂²×C₁₉	—	2	4	no	—
236	C₂²×C₁₉	—	4	4	no	—
237	C₂²×C₁₉	—	4	8	no	—
238	C₂²×C₁₉	—	4	8	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	8	8	no	—
241	C₂²×C₁₉	C₂×#121	1	2	yes	—
242	C₂²×C₁₉	C₂×#121	1	4	yes	—
243	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
244	C₄×C₁₉	—	2	4	no	—
245	C₄×C₁₉	—	4	8	no	—
246	C₄×C₁₉	—	4	4	no	—
247	C₄×C₁₉	C₂×#121	1	2	yes	—
248	C₄×C₁₉	C₂×#121	1	4	yes	—
249	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
250	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
251	C₂²×#41	C₂²×C₁₉	1	2	yes	—
252	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
253	#575	—	2	8	no	—
254	C₂×#137	C₂²×C₁₉	1	4	yes	complemented
255	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	4	yes	complemented
256	C₂×#135	C₂²×C₁₉	1	4	yes	—
257	C₂×#131	—	2	8	no	—
258	C₂×#131	C₂²×C₁₉	1	8	yes	complemented
259	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
260	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
261	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
262	C₂³×C₈	C₂²×C₁₉	1	2	yes	complemented
263	#537	C₂²×C₁₉	1	8	yes	—
264	#536	—	2	2	no	—
265	#536	C₂²×C₁₉	1	4	yes	complemented
266	#535	—	2	2	no	—
267	#535	C₂²×C₁₉	1	4	yes	complemented
268	#534	—	2	4	no	—
269	#532	—	2	4	no	—
270	#525	—	2	4	no	—
271	#525	C₂²×C₁₉	1	8	yes	complemented
272	C₂×#117	C₂²×C₁₉	1	2	yes	—
273	#470	C₂²×C₁₉	1	8	yes	complemented
274	#469	C₂²×C₁₉	1	8	yes	complemented
275	#468	C₂²×C₁₉	1	16	yes	complemented
276	#467	C₂²×C₁₉	1	8	yes	complemented
277	#466	C₂²×C₁₉	1	8	yes	complemented
278	#465	C₂²×C₁₉	1	16	yes	complemented
279	#428	C₂²×C₁₉	1	8	yes	complemented
280	#427	C₂²×C₁₉	1	4	yes	complemented
281	#416	C₂²×C₁₉	1	4	yes	complemented
282	#416	C₂²×C₁₉	1	4	yes	complemented
283	#416	C₂²×C₁₉	1	8	yes	complemented
284	C₂×#103	C₂²×C₁₉	1	4	yes	complemented
285	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
286	C₂×C₁₉	—	2	2	no	—
287	C₂×C₁₉	—	2	4	no	—
288	C₂×C₁₉	—	4	4	no	—
289	C₂×C₁₉	—	8	4	no	—
290	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
291	C₂×C₁₉	#3584	1	2	yes	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	—	2	2	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	2	4	no	—
296	C₂×#41	—	2	8	no	—
297	C₂×#41	—	2	8	no	—
298	C₂×#41	D₄×C₁₉	1	4	yes	—
299	C₂×#41	C₂³×C₁₉	1	4	yes	—
300	C₂×#41	C₂³×C₁₉	1	4	yes	—
301	C₂×#41	C₂³×C₁₉	1	4	yes	—
302	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
303	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	D₄×C₁₉	1	2	yes	—
306	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
307	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
310	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
311	#137	—	2	16	no	—
312	AGL(1,ℤ/8)	—	2	16	no	—
313	#135	—	2	16	no	—
314	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
315	C₂×SD₁₆	C₂³×C₁₉	1	8	yes	—
316	C₂×D₈	C₂³×C₁₉	1	4	yes	—
317	#131	—	2	32	no	—
318	C₂×M₁₆	—	2	8	no	—
319	C₂×M₁₆	D₄×C₁₉	1	8	yes	complemented
320	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
321	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
322	C₂²×C₈	—	2	4	no	—
323	C₂²×C₈	—	2	8	no	—
324	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
325	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
327	C₂²×C₈	C₂³×C₁₉	1	8	yes	—
328	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
329	C₄⋊Q₈	—	2	4	no	—
330	#127	—	2	4	no	—
331	#124	—	2	4	no	—
332	#124	—	2	4	no	—
333	#123	—	2	8	no	—
334	#123	—	2	8	no	—
335	C₂²⋊Q₈	—	2	8	no	—
336	C₂²⋊Q₈	C₂³×C₁₉	1	16	yes	—
337	#121	—	2	8	no	—
338	#121	—	2	16	no	—
339	#121	C₂³×C₁₉	1	16	yes	—
340	#120	—	2	8	no	—
341	#120	—	2	8	no	—
342	C₄×D₄	—	2	16	no	—
343	#117	—	2	2	no	—
344	#117	—	2	2	no	—
345	#117	C₂³×C₁₉	1	4	yes	—
346	#117	C₂³×C₁₉	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	#107	C₂³×C₁₉	1	8	yes	—
351	#106	C₂³×C₁₉	1	8	yes	—
352	#103	C₂³×C₁₉	1	8	yes	—
353	#103	C₂³×C₁₉	1	8	yes	—
354	#102	C₂³×C₁₉	1	8	yes	—
355	#102	C₂³×C₁₉	1	8	yes	—
356	C₁₉	#60453	1	1	yes	characteristic, direct product factor, Sylow
357	C₂⁴	—	2	2	no	—
358	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
359	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
360	#41	—	2	16	no	—
361	#41	—	2	8	no	—
362	#41	—	2	8	no	—
363	#41	—	2	8	no	—
364	#41	—	2	8	no	—
365	#41	—	2	8	no	—
366	#41	—	2	8	no	—
367	#41	—	4	8	no	—
368	#41	—	4	8	no	—
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
374	C₂×Q₈	C₂⁴×C₁₉	1	4	yes	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	16	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	C₂×D₄×C₁₉	1	8	yes	—
385	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
386	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	4	8	no	—
394	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
399	C₂²×C₄	#41×C₁₉	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
403	Q₁₆	—	2	8	no	—
404	SD₁₆	—	2	16	no	—
405	D₈	—	2	8	no	—
406	M₁₆	—	2	16	no	—
407	M₁₆	C₂×D₄×C₁₉	1	16	yes	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	8	no	—
411	C₂×C₈	—	2	16	no	—
412	C₂×C₈	C₂×D₄×C₁₉	1	8	yes	—
413	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
414	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
415	C₂×C₈	C₂⁴×C₁₉	1	4	yes	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	16	no	—
418	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	16	no	—
422	C₂²⋊C₄	—	2	16	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	4	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	8	4	no	—
431	C₂³	C₁₉×#121	1	4	yes	—
432	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
433	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
434	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
435	Q₈	—	2	8	no	—
436	Q₈	—	2	4	no	—
437	Q₈	—	2	4	no	—
438	Q₈	—	4	4	no	—
439	D₄	—	2	16	no	—
440	D₄	—	2	8	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	4	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	8	no	—
445	D₄	—	4	4	no	—
446	D₄	—	8	16	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	8	no	—
456	C₂×C₄	—	8	4	no	—
457	C₂×C₄	C₁₉×#121	1	8	yes	—
458	C₂×C₄	C₁₉×#121	1	4	yes	—
459	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
460	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
464	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
465	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
466	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	C₂²×D₄×C₁₉	1	8	yes	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	8	no	—
478	C₂²	—	8	8	no	—
479	C₂²	C₂×C₁₉×#121	1	2	yes	—
480	C₂²	C₂×C₁₉×#121	1	4	yes	—
481	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	8	no	—
485	C₄	C₂×C₁₉×#121	1	2	yes	—
486	C₄	C₂×C₁₉×#121	1	4	yes	—
487	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
488	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	2	4	no	—
491	C₂	—	4	4	no	—
492	C₂	—	8	4	no	—
493	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
494	C₂	C₁₉×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
socle	C₂²×C₁₉	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#575	C₂	semidirect
2. C₂²×C₁₉×#131	C₂	semidirect
3. C₁₉×#3449	C₂	semidirect
4. C₁₉×#3063	C₂	semidirect
5. C₁₉×#3062	C₂	semidirect
6. C₁₉×#3054	C₂	semidirect
7. C₁₉×#3050	C₂	semidirect
8. C₁₉×#2911	C₂	semidirect
9. C₂×C₁₉×#416	C₂	semidirect
13. C₂×C₁₉×#137	C₂²	semidirect
14. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₁₉×#131	C₂²	semidirect
19. C₂²×M₁₆×C₁₉	C₂²	semidirect
21. C₂³×C₈×C₁₉	C₂²	semidirect
24. C₁₉×#536	C₂²	semidirect
26. C₁₉×#535	C₂²	semidirect
30. C₁₉×#525	C₂²	semidirect
32. C₁₉×#470	C₂²	semidirect
33. C₁₉×#469	C₂²	semidirect
34. C₁₉×#468	C₂²	semidirect
35. C₁₉×#467	C₂²	semidirect
36. C₁₉×#466	C₂²	semidirect
37. C₁₉×#465	C₂²	semidirect
38. C₁₉×#428	C₂²	semidirect
39. C₁₉×#427	C₂²	semidirect
40. C₁₉×#416	C₂²	semidirect
41. C₁₉×#416	C₂²	semidirect
42. C₁₉×#416	C₂²	semidirect
43. C₂×C₁₉×#103	C₂²	semidirect
44. C₂×C₁₉×#102	C₂²	semidirect
72. C₂×M₁₆×C₁₉	D₄	semidirect
177. #60453	C₁₉	direct (N × H)
223. C₂×#575	C₂×C₁₉	semidirect
224. C₂²×#131	C₂×C₁₉	semidirect
225. #3449	C₂×C₁₉	semidirect
226. #3063	C₂×C₁₉	semidirect
227. #3062	C₂×C₁₉	semidirect
228. #3054	C₂×C₁₉	semidirect
229. #3050	C₂×C₁₉	semidirect
230. #2911	C₂×C₁₉	semidirect
231. C₂×#416	C₂×C₁₉	semidirect
254. C₂×#137	C₂²×C₁₉	semidirect
255. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
258. C₂×#131	C₂²×C₁₉	semidirect
260. C₂²×M₁₆	C₂²×C₁₉	semidirect
262. C₂³×C₈	C₂²×C₁₉	semidirect
265. #536	C₂²×C₁₉	semidirect
267. #535	C₂²×C₁₉	semidirect
271. #525	C₂²×C₁₉	semidirect
273. #470	C₂²×C₁₉	semidirect
274. #469	C₂²×C₁₉	semidirect
275. #468	C₂²×C₁₉	semidirect
276. #467	C₂²×C₁₉	semidirect
277. #466	C₂²×C₁₉	semidirect
278. #465	C₂²×C₁₉	semidirect
279. #428	C₂²×C₁₉	semidirect
280. #427	C₂²×C₁₉	semidirect
281. #416	C₂²×C₁₉	semidirect
282. #416	C₂²×C₁₉	semidirect
283. #416	C₂²×C₁₉	semidirect
284. C₂×#103	C₂²×C₁₉	semidirect
285. C₂×#102	C₂²×C₁₉	semidirect
319. C₂×M₁₆	D₄×C₁₉	semidirect
356. C₁₉	#60453	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#575	2
C₂²×C₁₉×#131	2
C₁₉×#3449	2
C₁₉×#3063	2
C₁₉×#3062	2
C₁₉×#3054	2
C₁₉×#3050	2
C₁₉×#2911	2
C₂×C₁₉×#416	2
#60453	19

Subgroups — C19×#60453 #18066412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#60453 #18066412