Subgroups — C₁₉×#32714 #18038673

Order 4864.

848 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2616	C₂	1	2	yes	maximal
2	C₁₉×#2077	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2076	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2036	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2035	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2035	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2001	C₂	1	2	yes	maximal, complemented
8	C₁₉×#2001	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1780	C₂	1	1	yes	maximal, characteristic
10	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
11	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
13	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#106	C₂²	1	2	yes	—
17	C₂×C₁₉×#103	C₂²	1	2	yes	—
18	C₂×C₁₉×#103	C₂²	1	2	yes	—
19	C₂×C₁₉×#103	C₂²	1	2	yes	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₁₉×#395	—	2	2	no	—
25	C₁₉×#394	—	2	2	no	—
26	C₁₉×#394	—	2	2	no	—
27	C₁₉×#394	—	2	2	no	—
28	C₁₉×#380	C₂²	1	2	yes	—
29	C₁₉×#380	C₂²	1	2	yes	—
30	C₁₉×#380	C₂²	1	2	yes	—
31	C₁₉×#340	C₂²	1	2	yes	—
32	C₁₉×#340	C₂²	1	1	yes	characteristic
33	C₁₉×#340	C₂²	1	1	yes	characteristic
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₂×#41×C₁₉	—	4	2	no	—
36	C₂×#41×C₁₉	—	4	1	no	—
37	C₂×#41×C₁₉	—	4	2	no	—
38	C₂×#41×C₁₉	—	4	1	no	—
39	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
41	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂×Q₁₆×C₁₉	—	4	2	no	—
46	C₂×Q₁₆×C₁₉	—	4	1	no	—
47	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×C₂²⋊Q₈	—	4	2	no	—
51	C₁₉×C₂²⋊Q₈	—	4	2	no	—
52	C₁₉×C₂²⋊Q₈	—	4	2	no	—
53	C₁₉×C₂²⋊Q₈	—	4	2	no	—
54	C₁₉×C₂²⋊Q₈	—	4	2	no	—
55	C₁₉×C₂²⋊Q₈	—	4	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
68	C₁₉×#107	—	4	1	no	—
69	C₁₉×#106	—	4	2	no	—
70	C₁₉×#103	—	4	2	no	—
71	C₁₉×#103	—	4	2	no	—
72	C₁₉×#103	—	4	2	no	—
73	C₁₉×C₂²⋊C₈	—	4	2	no	—
74	C₁₉×C₂²⋊C₈	—	4	1	no	—
75	C₁₉×C₂²⋊C₈	—	4	1	no	—
76	C₁₉×C₂²⋊C₈	—	4	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
82	#41×C₁₉	—	4	4	no	—
83	#41×C₁₉	—	4	8	no	—
84	#41×C₁₉	—	4	4	no	—
85	C₂×Q₈×C₁₉	—	2	2	no	—
86	C₂×Q₈×C₁₉	—	2	2	no	—
87	C₂×Q₈×C₁₉	—	2	2	no	—
88	C₂×Q₈×C₁₉	—	2	2	no	—
89	C₂×Q₈×C₁₉	—	2	2	no	—
90	C₂×Q₈×C₁₉	—	2	2	no	—
91	C₂×Q₈×C₁₉	—	4	2	no	—
92	C₂×Q₈×C₁₉	—	4	1	no	—
93	C₂×D₄×C₁₉	—	4	2	no	—
94	C₂×D₄×C₁₉	—	4	2	no	—
95	C₂×D₄×C₁₉	—	4	2	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	2	no	—
104	C₂²×C₄×C₁₉	—	2	2	no	—
105	C₂²×C₄×C₁₉	—	2	1	no	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	2	2	no	—
109	C₂²×C₄×C₁₉	—	2	2	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
115	Q₁₆×C₁₉	—	4	4	no	—
116	C₂×C₈×C₁₉	—	2	2	no	—
117	C₂×C₈×C₁₉	—	2	1	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	2	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	1	no	—
123	C₄⋊C₄×C₁₉	—	2	2	no	—
124	C₄⋊C₄×C₁₉	—	2	2	no	—
125	C₄⋊C₄×C₁₉	—	2	2	no	—
126	C₄⋊C₄×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	4	4	no	—
130	C₄⋊C₄×C₁₉	—	4	4	no	—
131	C₄⋊C₄×C₁₉	—	4	4	no	—
132	C₂²⋊C₄×C₁₉	—	4	4	no	—
133	C₂²⋊C₄×C₁₉	—	4	4	no	—
134	C₂²⋊C₄×C₁₉	—	4	4	no	—
135	C₂²⋊C₄×C₁₉	—	8	2	no	—
136	C₂²⋊C₄×C₁₉	—	8	2	no	—
137	C₂²⋊C₄×C₁₉	—	8	2	no	—
138	#32714	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂³×C₁₉	—	2	2	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	2	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	1	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	—	2	2	no	—
147	C₂³×C₁₉	—	2	1	no	—
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₁₉	—	4	4	no	—
153	Q₈×C₁₉	—	4	2	no	—
154	Q₈×C₁₉	—	4	2	no	—
155	Q₈×C₁₉	—	4	2	no	—
156	Q₈×C₁₉	—	4	2	no	—
157	D₄×C₁₉	—	4	4	no	—
158	D₄×C₁₉	—	4	8	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	2	no	—
161	C₂×C₄×C₁₉	—	2	2	no	—
162	C₂×C₄×C₁₉	—	2	2	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	4	1	no	—
165	C₂×C₄×C₁₉	—	4	2	no	—
166	C₂×C₄×C₁₉	—	4	2	no	—
167	C₂×C₄×C₁₉	—	4	2	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	2	no	—
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	4	2	no	—
174	C₂×C₄×C₁₉	—	4	2	no	—
175	C₂×C₄×C₁₉	—	4	2	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	2	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
184	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
186	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
187	C₈×C₁₉	—	4	2	no	—
188	C₈×C₁₉	—	4	1	no	—
189	C₈×C₁₉	—	4	1	no	—
190	#2616	C₂×C₁₉	1	2	yes	—
191	#2077	C₂×C₁₉	1	2	yes	complemented
192	#2076	C₂×C₁₉	1	1	yes	characteristic, complemented
193	#2036	C₂×C₁₉	1	2	yes	complemented
194	#2035	C₂×C₁₉	1	2	yes	complemented
195	#2035	C₂×C₁₉	1	2	yes	complemented
196	#2001	C₂×C₁₉	1	1	yes	characteristic, complemented
197	#2001	C₂×C₁₉	1	2	yes	complemented
198	#1780	C₂×C₁₉	1	1	yes	characteristic
199	C₂²×C₁₉	—	4	2	no	—
200	C₂²×C₁₉	—	4	2	no	—
201	C₂²×C₁₉	—	4	2	no	—
202	C₂²×C₁₉	—	4	2	no	—
203	C₂²×C₁₉	—	4	2	no	—
204	C₂²×C₁₉	—	4	2	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	—	4	1	no	—
207	C₂²×C₁₉	—	4	2	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	2	no	—
211	C₂²×C₁₉	#534	1	2	yes	—
212	C₂²×C₁₉	#534	1	1	yes	characteristic
213	C₂²×C₁₉	#577	1	2	yes	—
214	C₂²×C₁₉	#578	1	1	yes	characteristic
215	C₂²×C₁₉	#578	1	1	yes	characteristic
216	C₄×C₁₉	—	4	1	no	—
217	C₄×C₁₉	—	4	2	no	—
218	C₄×C₁₉	—	8	2	no	—
219	C₄×C₁₉	—	8	2	no	—
220	C₄×C₁₉	—	8	2	no	—
221	C₄×C₁₉	—	8	2	no	—
222	C₄×C₁₉	#560	1	2	yes	—
223	C₄×C₁₉	#560	1	1	yes	characteristic
224	C₄×C₁₉	H(3,𝔽₄)	1	1	yes	characteristic
225	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
226	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
227	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
228	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
229	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
230	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
231	C₂×#106	C₂²×C₁₉	1	2	yes	—
232	C₂×#103	C₂²×C₁₉	1	2	yes	—
233	C₂×#103	C₂²×C₁₉	1	2	yes	—
234	C₂×#103	C₂²×C₁₉	1	2	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
237	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
239	#395	—	2	2	no	—
240	#394	—	2	2	no	—
241	#394	—	2	2	no	—
242	#394	—	2	2	no	—
243	#380	C₂²×C₁₉	1	2	yes	—
244	#380	C₂²×C₁₉	1	2	yes	—
245	#380	C₂²×C₁₉	1	2	yes	—
246	#340	C₂²×C₁₉	1	2	yes	—
247	#340	C₂²×C₁₉	1	1	yes	characteristic
248	#340	C₂²×C₁₉	1	1	yes	characteristic
249	#340	C₂²×C₁₉	1	2	yes	—
250	C₂×C₁₉	—	8	1	no	—
251	C₂×C₁₉	—	8	2	no	—
252	C₂×C₁₉	#2812	1	1	yes	characteristic
253	C₂×C₁₉	#3201	1	2	yes	—
254	C₂×C₁₉	#3201	1	2	yes	—
255	C₂×C₁₉	#3202	1	1	yes	characteristic
256	C₂×C₁₉	#3204	1	1	yes	characteristic
257	C₂×#41	—	4	2	no	—
258	C₂×#41	—	4	1	no	—
259	C₂×#41	—	4	2	no	—
260	C₂×#41	—	4	1	no	—
261	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
262	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
263	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
264	C₂²×D₄	D₄×C₁₉	1	2	yes	—
265	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
267	C₂×Q₁₆	—	4	2	no	—
268	C₂×Q₁₆	—	4	1	no	—
269	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
271	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
272	C₂²⋊Q₈	—	4	2	no	—
273	C₂²⋊Q₈	—	4	2	no	—
274	C₂²⋊Q₈	—	4	2	no	—
275	C₂²⋊Q₈	—	4	2	no	—
276	C₂²⋊Q₈	—	4	2	no	—
277	C₂²⋊Q₈	—	4	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	#107	—	4	1	no	—
291	#106	—	4	2	no	—
292	#103	—	4	2	no	—
293	#103	—	4	2	no	—
294	#103	—	4	2	no	—
295	C₂²⋊C₈	—	4	1	no	—
296	C₂²⋊C₈	—	4	2	no	—
297	C₂²⋊C₈	—	4	2	no	—
298	C₂²⋊C₈	—	4	1	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	C₁₉	#32714	1	1	yes	characteristic, direct product factor, Sylow
303	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
304	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
305	#41	—	4	8	no	—
306	#41	—	4	4	no	—
307	#41	—	4	4	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	1	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
337	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
338	Q₁₆	—	4	4	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	4	no	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	—	8	2	no	—
359	C₂²⋊C₄	—	8	2	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
374	Q₈	—	4	4	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	8	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
408	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
409	C₈	—	4	2	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	2	no	—
424	C₂²	C₁₉×#534	1	2	yes	—
425	C₂²	C₁₉×#534	1	1	yes	characteristic
426	C₂²	C₁₉×#577	1	2	yes	—
427	C₂²	C₁₉×#578	1	1	yes	characteristic
428	C₂²	C₁₉×#578	1	1	yes	characteristic
429	C₄	—	4	1	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	2	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₁₉×#560	1	2	yes	—
436	C₄	C₁₉×#560	1	1	yes	characteristic
437	C₄	C₁₉×H(3,𝔽₄)	1	1	yes	characteristic
438	C₂	—	8	1	no	—
439	C₂	—	8	2	no	—
440	C₂	C₁₉×#2812	1	1	yes	characteristic
441	C₂	C₁₉×#3201	1	2	yes	—
442	C₂	C₁₉×#3201	1	2	yes	—
443	C₂	C₁₉×#3202	1	1	yes	characteristic
444	C₂	C₁₉×#3204	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×#41×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2077	C₂	semidirect
3. C₁₉×#2076	C₂	semidirect
4. C₁₉×#2036	C₂	semidirect
5. C₁₉×#2035	C₂	semidirect
6. C₁₉×#2035	C₂	semidirect
7. C₁₉×#2001	C₂	semidirect
8. C₁₉×#2001	C₂	semidirect
138. #32714	C₁₉	direct (N × H)
191. #2077	C₂×C₁₉	semidirect
192. #2076	C₂×C₁₉	semidirect
193. #2036	C₂×C₁₉	semidirect
194. #2035	C₂×C₁₉	semidirect
195. #2035	C₂×C₁₉	semidirect
196. #2001	C₂×C₁₉	semidirect
197. #2001	C₂×C₁₉	semidirect
302. C₁₉	#32714	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×#2616	2
C₁₉×#2077	2
C₁₉×#2076	2
C₁₉×#2036	2
C₁₉×#2035	2
C₁₉×#2001	2
C₁₉×#1780	2
#32714	19

Subgroups — C19×#32714 #18038673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32714 #18038673