Subgroups — C₁₉×#33350 #18039309

Order 4864.

1240 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3485	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2888	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2883	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2123	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2121	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2120	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#352	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
9	C₂²×#41×C₁₉	C₄	1	1	yes	characteristic, complemented
10	C₁₉×#568	—	2	1	no	—
11	C₁₉×#547	—	2	1	no	—
12	C₁₉×#547	—	2	2	no	—
13	C₁₉×#547	—	2	1	no	—
14	C₁₉×#546	—	2	1	no	—
15	C₁₉×#546	—	2	2	no	—
16	C₁₉×#546	—	2	1	no	—
17	C₁₉×#536	C₄	1	1	yes	characteristic, complemented
18	C₁₉×#536	C₂²	1	1	yes	characteristic
19	C₁₉×#534	C₄	1	2	yes	complemented
20	C₁₉×#534	C₂²	1	2	yes	—
21	C₁₉×#525	C₄	1	1	yes	characteristic, complemented
22	C₁₉×#525	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#123	C₄	1	2	yes	complemented
24	C₂×C₁₉×#123	C₂²	1	2	yes	—
25	C₁₉×#518	—	2	1	no	—
26	C₁₉×#518	C₄	1	1	yes	characteristic, complemented
27	C₁₉×#413	—	2	2	no	—
28	C₁₉×#413	C₂²	1	2	yes	—
29	C₂×C₁₉×#100	—	2	1	no	—
30	C₂×C₁₉×#100	C₂²	1	4	yes	—
31	C₁₉×#410	—	2	1	no	—
32	C₁₉×#410	C₂²	1	2	yes	—
33	C₂×C₁₉×#99	—	2	2	no	—
34	C₂×C₁₉×#99	C₂²	1	4	yes	—
35	C₁₉×#352	C₂²	1	4	yes	complemented
36	C₁₉×#352	C₂²	1	8	yes	complemented
37	C₁₉×AΣL(1,𝔽₁₆)	C₂²	1	4	yes	complemented
38	C₁₉×H(5,𝔽₂)	—	4	4	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	2	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	—	4	4	no	—
43	C₂×#41×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×#41×C₁₉	D₄	1	2	yes	—
45	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
46	C₂×#41×C₁₉	D₄	1	1	yes	characteristic
47	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
50	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	complemented
52	C₂²×D₄×C₁₉	D₄	1	2	yes	—
53	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	complemented
57	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic, complemented
58	C₁₉×#131	—	4	4	no	—
59	C₂×M₁₆×C₁₉	—	2	2	no	—
60	C₂×M₁₆×C₁₉	—	2	4	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×#124	—	2	1	no	—
64	C₁₉×#124	—	2	1	no	—
65	C₁₉×#123	—	2	2	no	—
66	C₁₉×#123	—	2	2	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	C₂×C₄	1	1	yes	characteristic, complemented
72	C₁₉×#123	C₂×C₄	1	2	yes	complemented
73	C₁₉×#123	C₂×C₄	1	2	yes	complemented
74	C₁₉×#123	C₂×C₄	1	2	yes	complemented
75	C₁₉×#123	C₂×C₄	1	2	yes	complemented
76	C₁₉×#123	C₂³	1	1	yes	characteristic
77	C₁₉×#123	C₂³	1	2	yes	—
78	C₁₉×C₂²⋊Q₈	—	2	1	no	—
79	C₁₉×C₂²⋊Q₈	—	2	1	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	1	no	—
82	C₁₉×C₂²⋊Q₈	—	2	1	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	1	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	—	2	2	no	—
89	C₁₉×#120	—	2	2	no	—
90	C₁₉×#120	—	2	2	no	—
91	C₁₉×#120	C₂×C₄	1	2	yes	complemented
92	C₁₉×#120	C₂×C₄	1	1	yes	characteristic, complemented
93	C₁₉×#120	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	1	no	—
96	C₄×D₄×C₁₉	—	2	1	no	—
97	C₄×D₄×C₁₉	—	2	2	no	—
98	C₄×D₄×C₁₉	—	2	1	no	—
99	C₄×D₄×C₁₉	—	2	1	no	—
100	C₄×D₄×C₁₉	—	4	4	no	—
101	C₁₉×#117	—	2	2	no	—
102	C₁₉×#117	C₂×C₄	1	1	yes	characteristic, complemented
103	C₁₉×#117	C₂×C₄	1	1	yes	characteristic, complemented
104	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
109	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
110	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
111	C₁₉×#101	—	2	2	no	—
112	C₁₉×#100	—	2	4	no	—
113	C₁₉×#100	C₂³	1	4	yes	—
114	C₁₉×#99	—	2	2	no	—
115	C₁₉×#99	—	2	4	no	—
116	C₁₉×#99	C₂³	1	4	yes	—
117	C₂⁴×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
119	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
120	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
121	#41×C₁₉	—	2	4	no	—
122	#41×C₁₉	—	4	2	no	—
123	#41×C₁₉	—	4	4	no	—
124	#41×C₁₉	—	4	2	no	—
125	#41×C₁₉	—	4	2	no	—
126	#41×C₁₉	—	4	8	no	—
127	#41×C₁₉	—	4	4	no	—
128	#41×C₁₉	—	4	4	no	—
129	C₂×Q₈×C₁₉	—	2	1	no	—
130	C₂×Q₈×C₁₉	—	2	1	no	—
131	C₂×Q₈×C₁₉	—	4	2	no	—
132	C₂×Q₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂×D₄×C₁₉	—	2	4	no	—
135	C₂×D₄×C₁₉	—	2	4	no	—
136	C₂×D₄×C₁₉	—	2	2	no	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	1	no	—
140	C₂×D₄×C₁₉	—	2	1	no	—
141	C₂×D₄×C₁₉	—	4	2	no	—
142	C₂×D₄×C₁₉	—	4	4	no	—
143	C₂×D₄×C₁₉	—	4	4	no	—
144	C₂×D₄×C₁₉	—	4	4	no	—
145	C₂×D₄×C₁₉	—	4	4	no	—
146	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
147	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
148	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
149	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
150	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
151	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
154	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₁₉	C₂⁴	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	1	no	—
163	C₂²×C₄×C₁₉	—	2	1	no	—
164	C₂²×C₄×C₁₉	—	4	2	no	—
165	C₂²×C₄×C₁₉	—	4	4	no	—
166	C₂²×C₄×C₁₉	—	4	4	no	—
167	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
168	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
169	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	M₁₆×C₁₉	—	2	4	no	—
176	M₁₆×C₁₉	—	4	4	no	—
177	M₁₆×C₁₉	—	4	2	no	—
178	C₂×C₈×C₁₉	—	4	4	no	—
179	C₂×C₈×C₁₉	—	4	2	no	—
180	C₄⋊C₄×C₁₉	—	2	1	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	2	2	no	—
184	C₄⋊C₄×C₁₉	—	2	2	no	—
185	C₄⋊C₄×C₁₉	—	2	1	no	—
186	C₄⋊C₄×C₁₉	—	2	1	no	—
187	C₄⋊C₄×C₁₉	—	2	1	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₄⋊C₄×C₁₉	—	4	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	1	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	2	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	1	no	—
198	C₂²⋊C₄×C₁₉	—	2	2	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	1	no	—
202	C₂²⋊C₄×C₁₉	—	2	4	no	—
203	C₂²⋊C₄×C₁₉	—	4	4	no	—
204	C₂²⋊C₄×C₁₉	C₂²×C₄	1	2	yes	—
205	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
206	C₂²⋊C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₁₉	—	2	1	no	—
208	C₄²×C₁₉	—	2	1	no	—
209	C₄²×C₁₉	—	4	2	no	—
210	#33350	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂³×C₁₉	—	2	4	no	—
212	C₂³×C₁₉	—	2	4	no	—
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	4	1	no	—
216	C₂³×C₁₉	—	8	2	no	—
217	C₂³×C₁₉	—	8	1	no	—
218	C₂³×C₁₉	—	8	2	no	—
219	C₂³×C₁₉	—	8	2	no	—
220	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
225	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₁₉	—	2	2	no	—
227	Q₈×C₁₉	—	4	1	no	—
228	Q₈×C₁₉	—	4	2	no	—
229	Q₈×C₁₉	—	4	2	no	—
230	D₄×C₁₉	—	2	4	no	—
231	D₄×C₁₉	—	2	4	no	—
232	D₄×C₁₉	—	2	4	no	—
233	D₄×C₁₉	—	2	2	no	—
234	D₄×C₁₉	—	2	2	no	—
235	D₄×C₁₉	—	4	1	no	—
236	D₄×C₁₉	—	4	2	no	—
237	D₄×C₁₉	—	4	2	no	—
238	D₄×C₁₉	—	4	1	no	—
239	D₄×C₁₉	—	4	2	no	—
240	D₄×C₁₉	—	4	1	no	—
241	D₄×C₁₉	—	4	4	no	—
242	D₄×C₁₉	—	4	4	no	—
243	D₄×C₁₉	—	8	2	no	—
244	D₄×C₁₉	—	8	1	no	—
245	D₄×C₁₉	—	8	1	no	—
246	D₄×C₁₉	#99	1	4	yes	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	1	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	1	no	—
254	C₂×C₄×C₁₉	—	2	1	no	—
255	C₂×C₄×C₁₉	—	2	2	no	—
256	C₂×C₄×C₁₉	—	4	2	no	—
257	C₂×C₄×C₁₉	—	4	2	no	—
258	C₂×C₄×C₁₉	—	4	2	no	—
259	C₂×C₄×C₁₉	—	4	4	no	—
260	C₂×C₄×C₁₉	—	4	4	no	—
261	C₂×C₄×C₁₉	—	4	2	no	—
262	C₂×C₄×C₁₉	—	4	1	no	—
263	C₂×C₄×C₁₉	—	4	2	no	—
264	C₂×C₄×C₁₉	—	4	4	no	—
265	C₂×C₄×C₁₉	—	8	2	no	—
266	C₂×C₄×C₁₉	—	8	2	no	—
267	C₂×C₄×C₁₉	—	16	4	no	—
268	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₈×C₁₉	—	4	4	no	—
274	#3485	C₂×C₁₉	1	1	yes	characteristic
275	#2888	C₂×C₁₉	1	1	yes	characteristic, complemented
276	#2883	C₂×C₁₉	1	1	yes	characteristic, complemented
277	#2123	C₂×C₁₉	1	2	yes	complemented
278	#2121	C₂×C₁₉	1	4	yes	complemented
279	#2120	C₂×C₁₉	1	2	yes	complemented
280	C₂×#352	C₂×C₁₉	1	4	yes	complemented
281	C₂²×C₁₉	—	2	1	no	—
282	C₂²×C₁₉	—	2	1	no	—
283	C₂²×C₁₉	—	2	1	no	—
284	C₂²×C₁₉	—	2	2	no	—
285	C₂²×C₁₉	—	2	2	no	—
286	C₂²×C₁₉	—	4	2	no	—
287	C₂²×C₁₉	—	4	2	no	—
288	C₂²×C₁₉	—	4	2	no	—
289	C₂²×C₁₉	—	4	1	no	—
290	C₂²×C₁₉	—	4	1	no	—
291	C₂²×C₁₉	—	4	1	no	—
292	C₂²×C₁₉	—	4	1	no	—
293	C₂²×C₁₉	—	4	1	no	—
294	C₂²×C₁₉	—	4	1	no	—
295	C₂²×C₁₉	—	8	4	no	—
296	C₂²×C₁₉	—	8	4	no	—
297	C₂²×C₁₉	—	8	2	no	—
298	C₂²×C₁₉	—	16	2	no	—
299	C₂²×C₁₉	C₂×#99	1	4	yes	—
300	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
301	C₄×C₁₉	—	2	1	no	—
302	C₄×C₁₉	—	2	1	no	—
303	C₄×C₁₉	—	2	1	no	—
304	C₄×C₁₉	—	2	2	no	—
305	C₄×C₁₉	—	4	1	no	—
306	C₄×C₁₉	—	4	2	no	—
307	C₄×C₁₉	—	4	1	no	—
308	C₄×C₁₉	—	4	1	no	—
309	C₄×C₁₉	—	4	2	no	—
310	C₄×C₁₉	—	8	4	no	—
311	C₄×C₁₉	C₂×#99	1	2	yes	—
312	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
313	C₂²×#41	C₄×C₁₉	1	1	yes	characteristic, complemented
314	#568	—	2	1	no	—
315	#547	—	2	1	no	—
316	#547	—	2	2	no	—
317	#547	—	2	1	no	—
318	#546	—	2	1	no	—
319	#546	—	2	2	no	—
320	#546	—	2	1	no	—
321	#536	C₄×C₁₉	1	1	yes	characteristic, complemented
322	#536	C₂²×C₁₉	1	1	yes	characteristic
323	#534	C₄×C₁₉	1	2	yes	complemented
324	#534	C₂²×C₁₉	1	2	yes	—
325	#525	C₄×C₁₉	1	1	yes	characteristic, complemented
326	#525	C₂²×C₁₉	1	1	yes	characteristic
327	C₂×#123	C₄×C₁₉	1	2	yes	complemented
328	C₂×#123	C₂²×C₁₉	1	2	yes	—
329	#518	—	2	1	no	—
330	#518	C₄×C₁₉	1	1	yes	characteristic, complemented
331	#413	—	2	2	no	—
332	#413	C₂²×C₁₉	1	2	yes	—
333	C₂×#100	—	2	1	no	—
334	C₂×#100	C₂²×C₁₉	1	4	yes	—
335	#410	—	2	1	no	—
336	#410	C₂²×C₁₉	1	2	yes	—
337	C₂×#99	—	2	2	no	—
338	C₂×#99	C₂²×C₁₉	1	4	yes	—
339	#352	C₂²×C₁₉	1	4	yes	complemented
340	#352	C₂²×C₁₉	1	8	yes	complemented
341	AΣL(1,𝔽₁₆)	C₂²×C₁₉	1	4	yes	complemented
342	C₂×C₁₉	—	2	1	no	—
343	C₂×C₁₉	—	2	4	no	—
344	C₂×C₁₉	—	4	1	no	—
345	C₂×C₁₉	—	4	1	no	—
346	C₂×C₁₉	—	4	2	no	—
347	C₂×C₁₉	—	4	2	no	—
348	C₂×C₁₉	—	4	1	no	—
349	C₂×C₁₉	—	8	1	no	—
350	C₂×C₁₉	C₂²×#99	1	1	yes	characteristic
351	H(5,𝔽₂)	—	4	4	no	—
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	4	4	no	—
356	C₂×#41	C₂×C₄×C₁₉	1	1	yes	characteristic
357	C₂×#41	D₄×C₁₉	1	2	yes	—
358	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
359	C₂×#41	D₄×C₁₉	1	1	yes	characteristic
360	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
361	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
362	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
363	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
364	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	complemented
365	C₂²×D₄	D₄×C₁₉	1	2	yes	—
366	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
367	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
368	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
369	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	complemented
370	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
371	#131	—	4	4	no	—
372	C₂×M₁₆	—	2	2	no	—
373	C₂×M₁₆	—	2	4	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	—	2	1	no	—
376	#124	—	2	1	no	—
377	#124	—	2	1	no	—
378	#123	—	2	2	no	—
379	#123	—	2	2	no	—
380	#123	—	2	2	no	—
381	#123	—	2	2	no	—
382	#123	—	2	2	no	—
383	#123	—	2	2	no	—
384	#123	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
385	#123	C₂×C₄×C₁₉	1	2	yes	complemented
386	#123	C₂×C₄×C₁₉	1	2	yes	complemented
387	#123	C₂×C₄×C₁₉	1	2	yes	complemented
388	#123	C₂×C₄×C₁₉	1	2	yes	complemented
389	#123	C₂³×C₁₉	1	1	yes	characteristic
390	#123	C₂³×C₁₉	1	2	yes	—
391	C₂²⋊Q₈	—	2	1	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	1	no	—
395	C₂²⋊Q₈	—	2	1	no	—
396	#121	—	2	1	no	—
397	#121	—	2	2	no	—
398	#121	—	2	2	no	—
399	#121	—	2	1	no	—
400	#121	—	2	2	no	—
401	#121	—	2	2	no	—
402	#120	—	2	2	no	—
403	#120	—	2	2	no	—
404	#120	C₂×C₄×C₁₉	1	2	yes	complemented
405	#120	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
406	#120	C₂³×C₁₉	1	1	yes	characteristic
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	4	4	no	—
414	#117	—	2	2	no	—
415	#117	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
416	#117	C₂×C₄×C₁₉	1	1	yes	characteristic, complemented
417	C₂×C₄⋊C₄	—	2	2	no	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₂²⋊C₄	—	2	2	no	—
421	C₂×C₂²⋊C₄	—	2	4	no	—
422	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
423	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	complemented
424	#101	—	2	2	no	—
425	#100	—	2	4	no	—
426	#100	C₂³×C₁₉	1	4	yes	—
427	#99	—	2	2	no	—
428	#99	—	2	4	no	—
429	#99	C₂³×C₁₉	1	4	yes	—
430	C₁₉	#33350	1	1	yes	characteristic, direct product factor, Sylow
431	C₂⁴	C₂²⋊C₄×C₁₉	1	2	yes	—
432	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
433	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
434	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
435	#41	—	2	4	no	—
436	#41	—	4	2	no	—
437	#41	—	4	4	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	—	4	8	no	—
441	#41	—	4	4	no	—
442	#41	—	4	4	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
447	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	4	4	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	4	4	no	—
460	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
461	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
462	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
463	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
464	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
465	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
466	C₂×D₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
467	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
468	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
469	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
470	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
471	C₂×D₄	C₂⁴×C₁₉	1	1	yes	characteristic
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	—	4	4	no	—
481	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
482	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
483	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
484	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
485	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
486	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
488	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
489	M₁₆	—	2	4	no	—
490	M₁₆	—	4	4	no	—
491	M₁₆	—	4	2	no	—
492	C₂×C₈	—	4	4	no	—
493	C₂×C₈	—	4	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	4	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	1	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	2	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	1	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₂²⋊C₄	C₂²×C₄×C₁₉	1	2	yes	—
519	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
520	C₂²⋊C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	4	2	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	8	2	no	—
530	C₂³	—	8	1	no	—
531	C₂³	—	8	2	no	—
532	C₂³	—	8	2	no	—
533	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
534	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
535	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
536	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
537	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
538	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
539	Q₈	—	2	2	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	4	2	no	—
542	Q₈	—	4	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	2	4	no	—
545	D₄	—	2	4	no	—
546	D₄	—	2	2	no	—
547	D₄	—	2	2	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	1	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	1	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	4	no	—
556	D₄	—	8	2	no	—
557	D₄	—	8	1	no	—
558	D₄	—	8	1	no	—
559	D₄	C₁₉×#99	1	4	yes	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	4	4	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	8	2	no	—
579	C₂×C₄	—	8	2	no	—
580	C₂×C₄	—	16	4	no	—
581	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
582	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
583	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
584	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
586	C₈	—	4	4	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	8	4	no	—
602	C₂²	—	8	4	no	—
603	C₂²	—	8	2	no	—
604	C₂²	—	16	2	no	—
605	C₂²	C₂×C₁₉×#99	1	4	yes	—
606	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	2	no	—
616	C₄	—	8	4	no	—
617	C₄	C₂×C₁₉×#99	1	2	yes	—
618	C₂	—	2	1	no	—
619	C₂	—	2	4	no	—
620	C₂	—	4	1	no	—
621	C₂	—	4	1	no	—
622	C₂	—	4	2	no	—
623	C₂	—	4	2	no	—
624	C₂	—	4	1	no	—
625	C₂	—	8	1	no	—
626	C₂	C₂²×C₁₉×#99	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	C₂²×#99
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂×D₄	C₂⁴×C₁₉
prime radical	C₁₉×#3485	C₂
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×D₄×C₁₉ ◁ C₂×C₁₉×H(5,𝔽₂) ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2888	C₂	semidirect
3. C₁₉×#2883	C₂	semidirect
4. C₁₉×#2123	C₂	semidirect
5. C₁₉×#2121	C₂	semidirect
6. C₁₉×#2120	C₂	semidirect
7. C₂×C₁₉×#352	C₂	semidirect
9. C₂²×#41×C₁₉	C₄	semidirect
17. C₁₉×#536	C₄	semidirect
19. C₁₉×#534	C₄	semidirect
21. C₁₉×#525	C₄	semidirect
23. C₂×C₁₉×#123	C₄	semidirect
26. C₁₉×#518	C₄	semidirect
35. C₁₉×#352	C₂²	semidirect
36. C₁₉×#352	C₂²	semidirect
37. C₁₉×AΣL(1,𝔽₁₆)	C₂²	semidirect
48. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
51. C₂²×D₄×C₁₉	C₂×C₄	semidirect
56. C₂³×C₄×C₁₉	C₂×C₄	semidirect
57. C₂³×C₄×C₁₉	C₂×C₄	semidirect
71. C₁₉×#123	C₂×C₄	semidirect
72. C₁₉×#123	C₂×C₄	semidirect
73. C₁₉×#123	C₂×C₄	semidirect
74. C₁₉×#123	C₂×C₄	semidirect
75. C₁₉×#123	C₂×C₄	semidirect
91. C₁₉×#120	C₂×C₄	semidirect
92. C₁₉×#120	C₂×C₄	semidirect
102. C₁₉×#117	C₂×C₄	semidirect
103. C₁₉×#117	C₂×C₄	semidirect
109. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
110. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
210. #33350	C₁₉	direct (N × H)
275. #2888	C₂×C₁₉	semidirect
276. #2883	C₂×C₁₉	semidirect
277. #2123	C₂×C₁₉	semidirect
278. #2121	C₂×C₁₉	semidirect
279. #2120	C₂×C₁₉	semidirect
280. C₂×#352	C₂×C₁₉	semidirect
313. C₂²×#41	C₄×C₁₉	semidirect
321. #536	C₄×C₁₉	semidirect
323. #534	C₄×C₁₉	semidirect
325. #525	C₄×C₁₉	semidirect
327. C₂×#123	C₄×C₁₉	semidirect
330. #518	C₄×C₁₉	semidirect
339. #352	C₂²×C₁₉	semidirect
340. #352	C₂²×C₁₉	semidirect
341. AΣL(1,𝔽₁₆)	C₂²×C₁₉	semidirect
361. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
364. C₂²×D₄	C₂×C₄×C₁₉	semidirect
369. C₂³×C₄	C₂×C₄×C₁₉	semidirect
370. C₂³×C₄	C₂×C₄×C₁₉	semidirect
384. #123	C₂×C₄×C₁₉	semidirect
385. #123	C₂×C₄×C₁₉	semidirect
386. #123	C₂×C₄×C₁₉	semidirect
387. #123	C₂×C₄×C₁₉	semidirect
388. #123	C₂×C₄×C₁₉	semidirect
404. #120	C₂×C₄×C₁₉	semidirect
405. #120	C₂×C₄×C₁₉	semidirect
415. #117	C₂×C₄×C₁₉	semidirect
416. #117	C₂×C₄×C₁₉	semidirect
422. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
423. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
430. C₁₉	#33350	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×#3485	2
C₁₉×#2888	2
C₁₉×#2883	2
C₁₉×#2123	2
C₁₉×#2121	2
C₁₉×#2120	2
C₂×C₁₉×#352	2
#33350	19

Subgroups — C19×#33350 #18039309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33350 #18039309