Subgroups — C₁₉×#32697 #18038656

Order 4864.

528 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2102	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#2082	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2070	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2049	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#2005	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1932	C₂	1	1	yes	maximal, characteristic
9	C₁₉×#1915	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1912	C₂	1	1	yes	maximal, characteristic
11	C₁₉×#1902	C₂	1	1	yes	maximal, characteristic
12	C₁₉×#1886	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₉×#1861	C₂	1	1	yes	maximal, characteristic
14	C₁₉×#1841	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#1830	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₉×#137	C₂²	1	1	yes	characteristic
17	C₁₉×#568	C₂²	1	1	yes	characteristic
18	C₁₉×#536	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₁₉×#519	C₂²	1	1	yes	characteristic
21	C₁₉×#430	C₂²	1	1	yes	characteristic
22	C₁₉×#430	C₂²	1	1	yes	characteristic
23	C₁₉×#430	C₂²	1	1	yes	characteristic
24	C₁₉×#423	C₂²	1	1	yes	characteristic
25	C₁₉×#421	C₂²	1	1	yes	characteristic
26	C₁₉×#421	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#104	C₂²	1	1	yes	characteristic
28	C₁₉×#419	C₂²	1	1	yes	characteristic
29	C₁₉×#419	C₂²	1	1	yes	characteristic
30	C₁₉×#419	C₂²	1	1	yes	characteristic
31	C₁₉×#413	C₂²	1	1	yes	characteristic
32	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
35	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
36	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
37	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#344	C₂²	1	1	yes	characteristic
40	C₁₉×#344	C₂²	1	1	yes	characteristic
41	C₁₉×#344	C₂²	1	1	yes	characteristic
42	C₁₉×#344	C₂²	1	1	yes	characteristic
43	C₁₉×#344	C₂²	1	1	yes	characteristic
44	C₁₉×#344	C₂²	1	1	yes	characteristic
45	C₁₉×#339	C₂²	1	1	yes	characteristic
46	C₁₉×#339	C₂²	1	1	yes	characteristic
47	C₁₉×#339	C₂²	1	1	yes	characteristic
48	C₁₉×#338	C₂²	1	1	yes	characteristic
49	C₁₉×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
50	C₁₉×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
51	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
54	C₁₉×#137	—	4	1	no	—
55	C₁₉×#137	—	4	1	no	—
56	C₂×Q₁₆×C₁₉	—	2	1	no	—
57	C₂×SD₁₆×C₁₉	—	2	1	no	—
58	C₁₉×#131	—	4	1	no	—
59	C₁₉×#131	—	4	1	no	—
60	C₂×M₁₆×C₁₉	—	4	1	no	—
61	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×C₄⋊Q₈	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	—	2	1	no	—
71	C₁₉×C₄⋊Q₈	—	2	1	no	—
72	C₁₉×C₄⋊Q₈	—	4	1	no	—
73	C₁₉×#124	—	2	1	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×C₂²⋊Q₈	—	4	1	no	—
76	C₄×Q₈×C₁₉	—	4	1	no	—
77	C₄×Q₈×C₁₉	—	4	1	no	—
78	C₁₉×#117	—	2	2	no	—
79	C₁₉×#117	C₂³	1	1	yes	characteristic
80	C₁₉×#117	C₂³	1	1	yes	characteristic
81	C₁₉×#117	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₁₉×#108	—	4	1	no	—
85	C₁₉×#108	—	4	1	no	—
86	C₁₉×#108	—	4	1	no	—
87	C₁₉×C₄⋊C₈	—	4	1	no	—
88	C₁₉×#104	—	2	1	no	—
89	C₁₉×#104	—	2	1	no	—
90	C₁₉×#104	—	4	1	no	—
91	C₁₉×#104	—	4	1	no	—
92	C₁₉×#103	—	4	1	no	—
93	C₁₉×#103	—	4	1	no	—
94	C₁₉×#103	—	4	1	no	—
95	C₁₉×#101	—	2	1	no	—
96	C₁₉×#101	—	4	1	no	—
97	C₁₉×#101	—	4	1	no	—
98	C₁₉×#101	—	4	1	no	—
99	C₁₉×#101	—	4	1	no	—
100	C₁₉×#101	—	4	1	no	—
101	C₁₉×#101	—	4	1	no	—
102	C₁₉×#100	—	2	1	no	—
103	C₁₉×#97	—	2	1	no	—
104	C₄×C₈×C₁₉	—	2	1	no	—
105	#41×C₁₉	—	2	1	no	—
106	#41×C₁₉	—	2	1	no	—
107	#41×C₁₉	—	2	1	no	—
108	#41×C₁₉	—	2	1	no	—
109	C₂×Q₈×C₁₉	—	2	1	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	1	no	—
112	C₂×Q₈×C₁₉	—	2	1	no	—
113	C₂×Q₈×C₁₉	—	2	1	no	—
114	C₂×Q₈×C₁₉	—	2	1	no	—
115	C₂×Q₈×C₁₉	—	2	1	no	—
116	C₂×Q₈×C₁₉	—	2	1	no	—
117	C₂×Q₈×C₁₉	—	2	1	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	1	no	—
121	C₂×Q₈×C₁₉	#41	1	1	yes	characteristic
122	C₂×D₄×C₁₉	—	2	1	no	—
123	C₂×D₄×C₁₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	#41	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
129	Q₁₆×C₁₉	—	4	2	no	—
130	SD₁₆×C₁₉	—	4	2	no	—
131	M₁₆×C₁₉	—	2	1	no	—
132	M₁₆×C₁₉	—	2	1	no	—
133	M₁₆×C₁₉	—	2	1	no	—
134	M₁₆×C₁₉	—	2	1	no	—
135	M₁₆×C₁₉	—	2	1	no	—
136	M₁₆×C₁₉	—	2	1	no	—
137	M₁₆×C₁₉	—	2	1	no	—
138	M₁₆×C₁₉	—	2	1	no	—
139	M₁₆×C₁₉	—	2	1	no	—
140	M₁₆×C₁₉	—	2	1	no	—
141	M₁₆×C₁₉	—	2	1	no	—
142	M₁₆×C₁₉	—	2	1	no	—
143	M₁₆×C₁₉	—	2	1	no	—
144	M₁₆×C₁₉	—	2	1	no	—
145	M₁₆×C₁₉	—	2	1	no	—
146	M₁₆×C₁₉	—	2	1	no	—
147	M₁₆×C₁₉	—	4	2	no	—
148	C₂×C₈×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	—	2	1	no	—
154	C₂×C₈×C₁₉	—	2	1	no	—
155	C₂×C₈×C₁₉	—	2	1	no	—
156	C₂×C₈×C₁₉	—	4	2	no	—
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	—	4	2	no	—
161	C₄⋊C₄×C₁₉	—	4	2	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	—	4	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	1	no	—
165	C₂²⋊C₄×C₁₉	—	2	1	no	—
166	C₂²⋊C₄×C₁₉	—	2	1	no	—
167	C₂²⋊C₄×C₁₉	—	4	2	no	—
168	C₄²×C₁₉	—	2	1	no	—
169	C₄²×C₁₉	—	2	1	no	—
170	C₄²×C₁₉	—	2	1	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	C₄²×C₁₉	—	4	2	no	—
173	C₄²×C₁₉	#41	1	1	yes	characteristic
174	C₄²×C₁₉	#41	1	1	yes	characteristic
175	#32697	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
178	Q₈×C₁₉	—	2	1	no	—
179	Q₈×C₁₉	—	2	1	no	—
180	Q₈×C₁₉	—	4	1	no	—
181	Q₈×C₁₉	—	4	1	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	Q₈×C₁₉	—	4	1	no	—
188	D₄×C₁₉	—	2	1	no	—
189	D₄×C₁₉	—	2	1	no	—
190	D₄×C₁₉	—	4	1	no	—
191	D₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	1	no	—
200	C₂×C₄×C₁₉	—	4	1	no	—
201	C₂×C₄×C₁₉	—	4	1	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
213	C₈×C₁₉	—	4	1	no	—
214	C₈×C₁₉	—	4	1	no	—
215	C₈×C₁₉	—	4	1	no	—
216	C₈×C₁₉	—	4	1	no	—
217	C₈×C₁₉	—	4	1	no	—
218	C₈×C₁₉	—	4	1	no	—
219	C₈×C₁₉	—	4	1	no	—
220	C₈×C₁₉	—	4	1	no	—
221	#2102	C₂×C₁₉	1	1	yes	characteristic, complemented
222	#2082	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#2082	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2070	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#2049	C₂×C₁₉	1	1	yes	characteristic
226	#2005	C₂×C₁₉	1	1	yes	characteristic
227	#1966	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#1932	C₂×C₁₉	1	1	yes	characteristic
229	#1915	C₂×C₁₉	1	1	yes	characteristic
230	#1912	C₂×C₁₉	1	1	yes	characteristic
231	#1902	C₂×C₁₉	1	1	yes	characteristic
232	#1886	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#1861	C₂×C₁₉	1	1	yes	characteristic
234	#1841	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1830	C₂×C₁₉	1	1	yes	characteristic, complemented
236	C₂²×C₁₉	—	4	1	no	—
237	C₂²×C₁₉	—	4	1	no	—
238	C₂²×C₁₉	—	8	1	no	—
239	C₂²×C₁₉	#538	1	1	yes	characteristic
240	C₂²×C₁₉	#551	1	1	yes	characteristic
241	C₂²×C₁₉	#551	1	1	yes	characteristic
242	C₄×C₁₉	—	2	2	no	—
243	C₄×C₁₉	—	4	1	no	—
244	C₄×C₁₉	—	4	2	no	—
245	C₄×C₁₉	—	4	1	no	—
246	C₄×C₁₉	—	8	1	no	—
247	C₄×C₁₉	—	8	1	no	—
248	C₄×C₁₉	—	8	1	no	—
249	C₄×C₁₉	—	8	1	no	—
250	C₄×C₁₉	#538	1	1	yes	characteristic
251	C₄×C₁₉	#540	1	1	yes	characteristic
252	C₄×C₁₉	#553	1	1	yes	characteristic
253	C₄×C₁₉	#560	1	1	yes	characteristic
254	C₂×#137	C₂²×C₁₉	1	1	yes	characteristic
255	#568	C₂²×C₁₉	1	1	yes	characteristic
256	#536	C₂²×C₁₉	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
258	#519	C₂²×C₁₉	1	1	yes	characteristic
259	#430	C₂²×C₁₉	1	1	yes	characteristic
260	#430	C₂²×C₁₉	1	1	yes	characteristic
261	#430	C₂²×C₁₉	1	1	yes	characteristic
262	#423	C₂²×C₁₉	1	1	yes	characteristic
263	#421	C₂²×C₁₉	1	1	yes	characteristic
264	#421	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#104	C₂²×C₁₉	1	1	yes	characteristic
266	#419	C₂²×C₁₉	1	1	yes	characteristic
267	#419	C₂²×C₁₉	1	1	yes	characteristic
268	#419	C₂²×C₁₉	1	1	yes	characteristic
269	#413	C₂²×C₁₉	1	1	yes	characteristic
270	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
271	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
272	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
274	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
276	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
277	#344	C₂²×C₁₉	1	1	yes	characteristic
278	#344	C₂²×C₁₉	1	1	yes	characteristic
279	#344	C₂²×C₁₉	1	1	yes	characteristic
280	#344	C₂²×C₁₉	1	1	yes	characteristic
281	#344	C₂²×C₁₉	1	1	yes	characteristic
282	#344	C₂²×C₁₉	1	1	yes	characteristic
283	#339	C₂²×C₁₉	1	1	yes	characteristic
284	#339	C₂²×C₁₉	1	1	yes	characteristic
285	#339	C₂²×C₁₉	1	1	yes	characteristic
286	#338	C₂²×C₁₉	1	1	yes	characteristic
287	H(3,ℤ/4)	C₂²×C₁₉	1	1	yes	characteristic
288	H(3,ℤ/4)	C₂²×C₁₉	1	1	yes	characteristic
289	C₂×C₁₉	—	2	1	no	—
290	C₂×C₁₉	—	2	1	no	—
291	C₂×C₁₉	—	2	1	no	—
292	C₂×C₁₉	—	8	1	no	—
293	C₂×C₁₉	#2749	1	1	yes	characteristic
294	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
295	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
296	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
297	#137	—	4	1	no	—
298	#137	—	4	1	no	—
299	C₂×Q₁₆	—	2	1	no	—
300	C₂×SD₁₆	—	2	1	no	—
301	#131	—	4	1	no	—
302	#131	—	4	1	no	—
303	C₂×M₁₆	—	4	1	no	—
304	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
306	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
307	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
309	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	4	1	no	—
316	#124	—	2	1	no	—
317	#123	—	2	2	no	—
318	C₂²⋊Q₈	—	4	1	no	—
319	C₄×Q₈	—	4	1	no	—
320	C₄×Q₈	—	4	1	no	—
321	#117	—	2	2	no	—
322	#117	C₂³×C₁₉	1	1	yes	characteristic
323	#117	C₂³×C₁₉	1	1	yes	characteristic
324	#117	C₂³×C₁₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
327	#108	—	4	1	no	—
328	#108	—	4	1	no	—
329	#108	—	4	1	no	—
330	C₄⋊C₈	—	4	1	no	—
331	#104	—	2	1	no	—
332	#104	—	2	1	no	—
333	#104	—	4	1	no	—
334	#104	—	4	1	no	—
335	#103	—	4	1	no	—
336	#103	—	4	1	no	—
337	#103	—	4	1	no	—
338	#101	—	2	1	no	—
339	#101	—	4	1	no	—
340	#101	—	4	1	no	—
341	#101	—	4	1	no	—
342	#101	—	4	1	no	—
343	#101	—	4	1	no	—
344	#101	—	4	1	no	—
345	#100	—	2	1	no	—
346	#97	—	2	1	no	—
347	C₄×C₈	—	2	1	no	—
348	C₁₉	#32697	1	1	yes	characteristic, direct product factor, Sylow
349	#41	—	2	1	no	—
350	#41	—	2	1	no	—
351	#41	—	2	1	no	—
352	#41	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	#41×C₁₉	1	1	yes	characteristic
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	#41×C₁₉	1	1	yes	characteristic
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	#41×C₁₉	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
373	Q₁₆	—	4	2	no	—
374	SD₁₆	—	4	2	no	—
375	M₁₆	—	2	1	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	1	no	—
378	M₁₆	—	2	1	no	—
379	M₁₆	—	2	1	no	—
380	M₁₆	—	2	1	no	—
381	M₁₆	—	2	1	no	—
382	M₁₆	—	2	1	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	1	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	2	1	no	—
389	M₁₆	—	2	1	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	4	2	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	4	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	4	2	no	—
417	C₄²	#41×C₁₉	1	1	yes	characteristic
418	C₄²	#41×C₁₉	1	1	yes	characteristic
419	C₂³	—	2	1	no	—
420	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
421	Q₈	—	2	1	no	—
422	Q₈	—	2	1	no	—
423	Q₈	—	4	1	no	—
424	Q₈	—	4	1	no	—
425	Q₈	—	4	1	no	—
426	Q₈	—	4	1	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	1	no	—
431	D₄	—	2	1	no	—
432	D₄	—	2	1	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
452	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
456	C₈	—	4	1	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	1	no	—
461	C₈	—	4	1	no	—
462	C₈	—	4	1	no	—
463	C₈	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	C₁₉×#538	1	1	yes	characteristic
468	C₂²	C₁₉×#551	1	1	yes	characteristic
469	C₂²	C₁₉×#551	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	4	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	1	no	—
476	C₄	—	8	1	no	—
477	C₄	—	8	1	no	—
478	C₄	C₁₉×#538	1	1	yes	characteristic
479	C₄	C₁₉×#540	1	1	yes	characteristic
480	C₄	C₁₉×#553	1	1	yes	characteristic
481	C₄	C₁₉×#560	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	8	1	no	—
486	C₂	C₁₉×#2749	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2749
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×#41×C₁₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2102	C₂	semidirect
2. C₁₉×#2082	C₂	semidirect
3. C₁₉×#2082	C₂	semidirect
4. C₁₉×#2070	C₂	semidirect
7. C₁₉×#1966	C₂	semidirect
12. C₁₉×#1886	C₂	semidirect
14. C₁₉×#1841	C₂	semidirect
15. C₁₉×#1830	C₂	semidirect
175. #32697	C₁₉	direct (N × H)
221. #2102	C₂×C₁₉	semidirect
222. #2082	C₂×C₁₉	semidirect
223. #2082	C₂×C₁₉	semidirect
224. #2070	C₂×C₁₉	semidirect
227. #1966	C₂×C₁₉	semidirect
232. #1886	C₂×C₁₉	semidirect
234. #1841	C₂×C₁₉	semidirect
235. #1830	C₂×C₁₉	semidirect
348. C₁₉	#32697	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×#2102	2
C₁₉×#2082	2
C₁₉×#2070	2
C₁₉×#2049	2
C₁₉×#2005	2
C₁₉×#1966	2
C₁₉×#1932	2
C₁₉×#1915	2
C₁₉×#1912	2
C₁₉×#1902	2
C₁₉×#1886	2
C₁₉×#1861	2
C₁₉×#1841	2
C₁₉×#1830	2
#32697	19

Subgroups — C19×#32697 #18038656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32697 #18038656