Subgroups — C₁₉×#32922 #18038881

Order 4864.

1418 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3039	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#455	C₂	1	2	yes	maximal
4	C₁₉×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1885	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1882	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1806	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1800	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#137	C₂²	1	4	yes	—
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₉×#124	C₂²	1	2	yes	—
13	C₁₉×#520	—	2	2	no	—
14	C₁₉×#520	C₂²	1	2	yes	—
15	C₁₉×#518	—	2	2	no	—
16	C₁₉×#518	—	2	2	no	—
17	C₁₉×#518	C₂²	1	1	yes	characteristic
18	C₄×#41×C₁₉	—	2	2	no	—
19	C₄×#41×C₁₉	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₉	—	2	2	no	—
21	C₂×C₄×D₄×C₁₉	—	2	2	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#462	—	2	2	no	—
24	C₁₉×#462	—	2	2	no	—
25	C₁₉×#461	—	2	2	no	—
26	C₁₉×#461	—	2	2	no	—
27	C₁₉×#455	—	2	8	no	—
28	C₁₉×#423	C₂²	1	2	yes	complemented
29	C₂×C₁₉×#104	C₂²	1	4	yes	—
30	C₁₉×#419	C₂²	1	4	yes	complemented
31	C₂×C₁₉×#100	C₂²	1	2	yes	—
32	C₁₉×#397	—	2	2	no	—
33	C₁₉×#391	C₂²	1	2	yes	complemented
34	C₁₉×#380	—	2	2	no	—
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₁₉×#343	C₂²	1	2	yes	complemented
37	C₁₉×#339	C₂²	1	4	yes	complemented
38	C₁₉×H(5,𝔽₂)	—	2	4	no	—
39	C₁₉×H(5,𝔽₂)	—	2	2	no	—
40	C₁₉×H(5,𝔽₂)	D₄	1	4	yes	—
41	C₂×#41×C₁₉	—	2	2	no	—
42	C₂×#41×C₁₉	C₂³	1	2	yes	—
43	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	D₄	1	2	yes	—
49	C₁₉×#137	—	2	8	no	—
50	C₁₉×#137	—	2	8	no	—
51	C₂×Q₁₆×C₁₉	—	2	4	no	—
52	C₂×SD₁₆×C₁₉	—	2	4	no	—
53	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
54	C₁₉×C₄⋊Q₈	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₁₉×#124	—	2	4	no	—
57	C₁₉×#124	—	2	4	no	—
58	C₄×Q₈×C₁₉	—	2	2	no	—
59	C₄×Q₈×C₁₉	D₄	1	2	yes	—
60	C₄×Q₈×C₁₉	D₄	1	2	yes	—
61	C₄×D₄×C₁₉	—	2	4	no	—
62	C₄×D₄×C₁₉	—	2	4	no	—
63	C₄×D₄×C₁₉	—	2	4	no	—
64	C₄×D₄×C₁₉	—	2	4	no	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	2	no	—
67	C₄×D₄×C₁₉	—	2	4	no	—
68	C₄×D₄×C₁₉	—	2	2	no	—
69	C₄×D₄×C₁₉	—	2	2	no	—
70	C₄×D₄×C₁₉	—	2	2	no	—
71	C₄×D₄×C₁₉	—	2	2	no	—
72	C₄×D₄×C₁₉	—	2	2	no	—
73	C₄×D₄×C₁₉	D₄	1	2	yes	—
74	C₄×D₄×C₁₉	D₄	1	2	yes	—
75	C₁₉×#117	—	2	4	no	—
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	2	no	—
78	C₁₉×#117	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
89	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
90	C₂×C₄²×C₁₉	—	2	2	no	—
91	C₂×C₄²×C₁₉	—	2	2	no	—
92	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
94	C₁₉×C₄⋊C₈	—	2	2	no	—
95	C₁₉×C₄⋊C₈	—	2	2	no	—
96	C₁₉×#104	—	2	8	no	—
97	C₁₉×#103	—	2	4	no	—
98	C₁₉×#103	—	2	4	no	—
99	C₁₉×#100	—	2	4	no	—
100	C₁₉×#95	—	2	1	no	—
101	C₁₉×#95	—	2	4	no	—
102	C₂⁴×C₁₉	—	2	2	no	—
103	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
104	#41×C₁₉	—	2	8	no	—
105	#41×C₁₉	—	2	8	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	—	2	2	no	—
108	#41×C₁₉	C₂×D₄	1	4	yes	—
109	#41×C₁₉	#41	1	4	yes	—
110	C₂×Q₈×C₁₉	—	2	2	no	—
111	C₂×Q₈×C₁₉	—	2	4	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	4	no	—
114	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₁₉	—	2	4	no	—
116	C₂×D₄×C₁₉	—	2	8	no	—
117	C₂×D₄×C₁₉	—	2	8	no	—
118	C₂×D₄×C₁₉	—	2	8	no	—
119	C₂×D₄×C₁₉	—	2	2	no	—
120	C₂×D₄×C₁₉	—	2	8	no	—
121	C₂×D₄×C₁₉	—	2	2	no	—
122	C₂×D₄×C₁₉	—	2	2	no	—
123	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₁₉	#41	1	2	yes	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	4	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	2	no	—
132	C₂²×C₄×C₁₉	—	2	2	no	—
133	C₂²×C₄×C₁₉	—	2	2	no	—
134	C₂²×C₄×C₁₉	—	2	2	no	—
135	C₂²×C₄×C₁₉	—	2	2	no	—
136	C₂²×C₄×C₁₉	—	2	2	no	—
137	C₂²×C₄×C₁₉	—	4	4	no	—
138	C₂²×C₄×C₁₉	—	8	4	no	—
139	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
143	Q₁₆×C₁₉	—	4	8	no	—
144	SD₁₆×C₁₉	—	4	8	no	—
145	M₁₆×C₁₉	—	2	4	no	—
146	M₁₆×C₁₉	—	2	4	no	—
147	C₂×C₈×C₁₉	—	2	4	no	—
148	C₄⋊C₄×C₁₉	—	2	4	no	—
149	C₄⋊C₄×C₁₉	—	2	2	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	2	2	no	—
152	C₄⋊C₄×C₁₉	—	4	2	no	—
153	C₄⋊C₄×C₁₉	—	4	2	no	—
154	C₄⋊C₄×C₁₉	—	4	1	no	—
155	C₄⋊C₄×C₁₉	—	4	1	no	—
156	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₁₉	—	2	4	no	—
159	C₂²⋊C₄×C₁₉	—	2	4	no	—
160	C₂²⋊C₄×C₁₉	—	2	2	no	—
161	C₂²⋊C₄×C₁₉	—	2	2	no	—
162	C₂²⋊C₄×C₁₉	—	2	2	no	—
163	C₂²⋊C₄×C₁₉	—	2	4	no	—
164	C₂²⋊C₄×C₁₉	—	4	8	no	—
165	C₄²×C₁₉	—	2	4	no	—
166	C₄²×C₁₉	—	2	2	no	—
167	C₄²×C₁₉	—	2	2	no	—
168	C₄²×C₁₉	—	2	2	no	—
169	C₄²×C₁₉	—	2	2	no	—
170	C₄²×C₁₉	—	2	2	no	—
171	C₄²×C₁₉	C₂×D₄	1	2	yes	—
172	C₄²×C₁₉	C₂×D₄	1	2	yes	—
173	#32922	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂³×C₁₉	—	2	8	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	2	no	—
177	C₂³×C₁₉	—	2	2	no	—
178	C₂³×C₁₉	—	4	2	no	—
179	C₂³×C₁₉	—	4	2	no	—
180	C₂³×C₁₉	—	8	2	no	—
181	C₂³×C₁₉	—	8	2	no	—
182	C₂³×C₁₉	#121	1	4	yes	—
183	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₁₉	—	2	2	no	—
185	Q₈×C₁₉	—	4	4	no	—
186	Q₈×C₁₉	—	4	4	no	—
187	Q₈×C₁₉	#121	1	4	yes	—
188	D₄×C₁₉	—	2	16	no	—
189	D₄×C₁₉	—	2	4	no	—
190	D₄×C₁₉	—	2	4	no	—
191	D₄×C₁₉	—	2	4	no	—
192	D₄×C₁₉	—	2	2	no	—
193	D₄×C₁₉	—	2	4	no	—
194	D₄×C₁₉	#121	1	4	yes	—
195	C₂×C₄×C₁₉	—	2	8	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	8	2	no	—
214	C₂×C₄×C₁₉	—	8	2	no	—
215	C₂×C₄×C₁₉	—	8	2	no	—
216	C₂×C₄×C₁₉	—	8	4	no	—
217	C₂×C₄×C₁₉	—	8	2	no	—
218	C₂×C₄×C₁₉	#120	1	2	yes	—
219	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
220	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
224	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
225	C₈×C₁₉	—	4	4	no	—
226	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
227	#3039	C₂×C₁₉	1	2	yes	complemented
228	C₂×#455	C₂×C₁₉	1	2	yes	—
229	#2547	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#1885	C₂×C₁₉	1	2	yes	complemented
231	#1882	C₂×C₁₉	1	4	yes	complemented
232	#1806	C₂×C₁₉	1	2	yes	complemented
233	#1800	C₂×C₁₉	1	1	yes	characteristic, complemented
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	4	no	—
237	C₂²×C₁₉	—	2	4	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	4	2	no	—
241	C₂²×C₁₉	—	4	2	no	—
242	C₂²×C₁₉	—	4	2	no	—
243	C₂²×C₁₉	—	8	2	no	—
244	C₂²×C₁₉	—	8	8	no	—
245	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
246	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
247	C₂²×C₁₉	#525	1	1	yes	characteristic
248	C₄×C₁₉	—	2	4	no	—
249	C₄×C₁₉	—	2	1	no	—
250	C₄×C₁₉	—	2	2	no	—
251	C₄×C₁₉	—	4	2	no	—
252	C₄×C₁₉	—	4	2	no	—
253	C₄×C₁₉	—	4	2	no	—
254	C₄×C₁₉	—	8	2	no	—
255	C₄×C₁₉	—	8	2	no	—
256	C₄×C₁₉	#455	1	2	yes	complemented
257	C₄×C₁₉	C₂×#121	1	2	yes	—
258	C₄×C₁₉	#525	1	2	yes	—
259	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
260	C₂×#137	C₂²×C₁₉	1	4	yes	—
261	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
262	C₂×#124	C₂²×C₁₉	1	2	yes	—
263	#520	—	2	2	no	—
264	#520	C₂²×C₁₉	1	2	yes	—
265	#518	—	2	2	no	—
266	#518	—	2	2	no	—
267	#518	C₂²×C₁₉	1	1	yes	characteristic
268	C₄×#41	—	2	2	no	—
269	C₄×#41	C₂²×C₁₉	1	2	yes	—
270	C₂×C₄×D₄	—	2	2	no	—
271	C₂×C₄×D₄	—	2	2	no	—
272	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
273	#462	—	2	2	no	—
274	#462	—	2	2	no	—
275	#461	—	2	2	no	—
276	#461	—	2	2	no	—
277	#455	—	2	8	no	—
278	#423	C₂²×C₁₉	1	2	yes	complemented
279	C₂×#104	C₂²×C₁₉	1	4	yes	—
280	#419	C₂²×C₁₉	1	4	yes	complemented
281	C₂×#100	C₂²×C₁₉	1	2	yes	—
282	#397	—	2	2	no	—
283	#391	C₂²×C₁₉	1	2	yes	complemented
284	#380	—	2	2	no	—
285	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
286	#343	C₂²×C₁₉	1	2	yes	complemented
287	#339	C₂²×C₁₉	1	4	yes	complemented
288	C₂×C₁₉	—	2	1	no	—
289	C₂×C₁₉	—	2	1	no	—
290	C₂×C₁₉	—	4	4	no	—
291	C₂×C₁₉	—	4	4	no	—
292	C₂×C₁₉	#2847	1	1	yes	characteristic
293	C₂×C₁₉	C₂×#455	1	1	yes	characteristic
294	C₂×C₁₉	#3022	1	1	yes	characteristic
295	H(5,𝔽₂)	—	2	4	no	—
296	H(5,𝔽₂)	—	2	2	no	—
297	H(5,𝔽₂)	D₄×C₁₉	1	4	yes	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	C₂³×C₁₉	1	2	yes	—
300	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	D₄×C₁₉	1	2	yes	—
306	#137	—	2	8	no	—
307	#137	—	2	8	no	—
308	C₂×Q₁₆	—	2	4	no	—
309	C₂×SD₁₆	—	2	4	no	—
310	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	2	no	—
313	#124	—	2	4	no	—
314	#124	—	2	4	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	D₄×C₁₉	1	2	yes	—
317	C₄×Q₈	D₄×C₁₉	1	2	yes	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	4	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	D₄×C₁₉	1	2	yes	—
331	C₄×D₄	D₄×C₁₉	1	2	yes	—
332	#117	—	2	4	no	—
333	#117	—	2	2	no	—
334	#117	—	2	2	no	—
335	#117	C₂³×C₁₉	1	2	yes	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
350	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
351	C₄⋊C₈	—	2	2	no	—
352	C₄⋊C₈	—	2	2	no	—
353	#104	—	2	8	no	—
354	#103	—	2	4	no	—
355	#103	—	2	4	no	—
356	#100	—	2	4	no	—
357	#95	—	2	1	no	—
358	#95	—	2	4	no	—
359	C₁₉	#32922	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	—	2	2	no	—
361	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
362	#41	—	2	8	no	—
363	#41	—	2	8	no	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	C₂×D₄×C₁₉	1	4	yes	—
367	#41	#41×C₁₉	1	4	yes	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
382	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
383	C₂×D₄	#41×C₁₉	1	2	yes	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	8	4	no	—
397	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
400	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
401	Q₁₆	—	4	8	no	—
402	SD₁₆	—	4	8	no	—
403	M₁₆	—	2	4	no	—
404	M₁₆	—	2	4	no	—
405	C₂×C₈	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
415	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	4	8	no	—
423	C₄²	—	2	4	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	C₂×D₄×C₁₉	1	2	yes	—
430	C₄²	C₂×D₄×C₁₉	1	2	yes	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	8	2	no	—
438	C₂³	—	8	2	no	—
439	C₂³	C₁₉×#121	1	4	yes	—
440	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
441	Q₈	—	2	2	no	—
442	Q₈	—	4	4	no	—
443	Q₈	—	4	4	no	—
444	Q₈	C₁₉×#121	1	4	yes	—
445	D₄	—	2	16	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	2	4	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	4	no	—
451	D₄	C₁₉×#121	1	4	yes	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	2	no	—
471	C₂×C₄	—	8	2	no	—
472	C₂×C₄	—	8	4	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	8	2	no	—
475	C₂×C₄	C₁₉×#120	1	2	yes	—
476	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
477	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
480	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
481	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
482	C₈	—	4	4	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	8	no	—
494	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
495	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
496	C₂²	C₁₉×#525	1	1	yes	characteristic
497	C₄	—	2	1	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	4	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	8	2	no	—
504	C₄	—	8	2	no	—
505	C₄	C₁₉×#455	1	2	yes	complemented
506	C₄	C₂×C₁₉×#121	1	2	yes	—
507	C₄	C₁₉×#525	1	2	yes	—
508	C₂	—	2	1	no	—
509	C₂	—	2	1	no	—
510	C₂	—	4	4	no	—
511	C₂	—	4	4	no	—
512	C₂	C₁₉×#2847	1	1	yes	characteristic
513	C₂	C₂×C₁₉×#455	1	1	yes	characteristic
514	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3039	C₂	semidirect
4. C₁₉×#2547	C₂	semidirect
5. C₁₉×#1885	C₂	semidirect
6. C₁₉×#1882	C₂	semidirect
7. C₁₉×#1806	C₂	semidirect
8. C₁₉×#1800	C₂	semidirect
11. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
28. C₁₉×#423	C₂²	semidirect
30. C₁₉×#419	C₂²	semidirect
33. C₁₉×#391	C₂²	semidirect
35. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
36. C₁₉×#343	C₂²	semidirect
37. C₁₉×#339	C₂²	semidirect
173. #32922	C₁₉	direct (N × H)
227. #3039	C₂×C₁₉	semidirect
229. #2547	C₂×C₁₉	semidirect
230. #1885	C₂×C₁₉	semidirect
231. #1882	C₂×C₁₉	semidirect
232. #1806	C₂×C₁₉	semidirect
233. #1800	C₂×C₁₉	semidirect
256. C₄×C₁₉	#455	semidirect
261. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
278. #423	C₂²×C₁₉	semidirect
280. #419	C₂²×C₁₉	semidirect
283. #391	C₂²×C₁₉	semidirect
285. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
286. #343	C₂²×C₁₉	semidirect
287. #339	C₂²×C₁₉	semidirect
359. C₁₉	#32922	direct (N × H)
505. C₄	C₁₉×#455	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₉×H(5,𝔽₂)	2
C₁₉×#3039	2
C₂×C₁₉×#455	2
C₁₉×#2547	2
C₁₉×#1885	2
C₁₉×#1882	2
C₁₉×#1806	2
C₁₉×#1800	2
#32922	19

Subgroups — C19×#32922 #18038881

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32922 #18038881