Subgroups — C₁₉×#32978 #18038937

Order 4864.

1812 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#480	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2847	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1874	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1852	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1823	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1779	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×C₄×C₁₉	—	2	1	no	—
9	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×#121	C₂²	1	2	yes	—
12	C₂×C₁₉×#120	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₁₉	—	2	2	no	—
15	C₂²×C₄⋊C₄×C₁₉	—	2	8	no	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
18	C₁₉×#480	—	2	8	no	—
19	C₂×C₁₉×#107	C₂²	1	4	yes	complemented
20	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
21	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₉×C₂²⋊C₈	C₂²	1	4	yes	—
23	C₁₉×#386	—	2	1	no	—
24	C₁₉×#386	—	2	2	no	—
25	C₁₉×#380	C₂²	1	1	yes	characteristic
26	C₁₉×#380	C₂²	1	2	yes	—
27	C₁₉×#340	C₂²	1	8	yes	complemented
28	C₂⁵×C₁₉	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	2	no	—
31	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₁₉	—	2	4	no	—
33	C₂³×C₄×C₁₉	—	2	8	no	—
34	C₂³×C₄×C₁₉	—	2	8	no	—
35	C₂³×C₄×C₁₉	—	2	4	no	—
36	C₂³×C₄×C₁₉	—	2	2	no	—
37	C₂³×C₄×C₁₉	—	4	4	no	—
38	C₂³×C₄×C₁₉	—	4	4	no	—
39	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	D₄	1	2	yes	—
41	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
44	C₁₉×#121	—	2	4	no	—
45	C₁₉×#121	—	2	8	no	—
46	C₁₉×#120	—	4	4	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	16	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	16	no	—
53	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	complemented
54	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
61	C₁₉×#107	—	2	8	no	—
62	C₁₉×#102	—	2	8	no	—
63	C₁₉×C₂²⋊C₈	—	2	4	no	—
64	C₁₉×C₂²⋊C₈	—	2	8	no	—
65	C₁₉×#95	—	2	1	no	—
66	C₁₉×#95	—	2	2	no	—
67	C₂⁴×C₁₉	—	2	2	no	—
68	C₂⁴×C₁₉	—	2	4	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	4	no	—
71	C₂⁴×C₁₉	—	2	1	no	—
72	C₂⁴×C₁₉	D₈	1	4	yes	—
73	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	4	no	—
77	C₂×D₄×C₁₉	—	4	2	no	—
78	C₂×D₄×C₁₉	—	4	4	no	—
79	C₂×D₄×C₁₉	—	4	2	no	—
80	C₂×D₄×C₁₉	—	4	4	no	—
81	C₂×D₄×C₁₉	—	4	2	no	—
82	C₂×D₄×C₁₉	—	4	4	no	—
83	C₂²×C₄×C₁₉	—	2	32	no	—
84	C₂²×C₄×C₁₉	—	2	2	no	—
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	4	no	—
87	C₂²×C₄×C₁₉	—	2	4	no	—
88	C₂²×C₄×C₁₉	—	2	4	no	—
89	C₂²×C₄×C₁₉	—	2	4	no	—
90	C₂²×C₄×C₁₉	—	2	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	16	no	—
93	C₂²×C₄×C₁₉	—	2	8	no	—
94	C₂²×C₄×C₁₉	—	2	4	no	—
95	C₂²×C₄×C₁₉	—	2	1	no	—
96	C₂²×C₄×C₁₉	—	2	2	no	—
97	C₂²×C₄×C₁₉	—	4	8	no	—
98	C₂²×C₄×C₁₉	—	4	32	no	—
99	C₂²×C₄×C₁₉	—	4	8	no	—
100	C₂²×C₄×C₁₉	—	4	4	no	—
101	C₂²×C₄×C₁₉	—	4	4	no	—
102	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₉	#41	1	8	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₁₉	—	2	4	no	—
108	C₂×C₈×C₁₉	—	2	8	no	—
109	C₄⋊C₄×C₁₉	—	2	16	no	—
110	C₄⋊C₄×C₁₉	—	2	8	no	—
111	C₄⋊C₄×C₁₉	—	2	4	no	—
112	C₄⋊C₄×C₁₉	—	2	2	no	—
113	C₄⋊C₄×C₁₉	—	2	4	no	—
114	C₄⋊C₄×C₁₉	C₂×D₄	1	8	yes	—
115	C₂²⋊C₄×C₁₉	—	4	2	no	—
116	C₂²⋊C₄×C₁₉	—	4	4	no	—
117	C₂²⋊C₄×C₁₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₉	—	4	4	no	—
119	#32978	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂³×C₁₉	—	2	8	no	—
121	C₂³×C₁₉	—	2	16	no	—
122	C₂³×C₁₉	—	2	8	no	—
123	C₂³×C₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	2	no	—
125	C₂³×C₁₉	—	2	2	no	—
126	C₂³×C₁₉	—	2	2	no	—
127	C₂³×C₁₉	—	2	2	no	—
128	C₂³×C₁₉	—	2	2	no	—
129	C₂³×C₁₉	—	2	8	no	—
130	C₂³×C₁₉	—	2	16	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	1	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	#120	1	2	yes	—
137	C₂³×C₁₉	#123	1	4	yes	—
138	C₂³×C₁₉	C₂×D₈	1	2	yes	—
139	C₂³×C₁₉	C₂×D₈	1	4	yes	—
140	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
141	C₂³×C₁₉	#137	1	4	yes	—
142	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
143	D₄×C₁₉	—	4	4	no	—
144	D₄×C₁₉	—	8	4	no	—
145	D₄×C₁₉	—	8	8	no	—
146	C₂×C₄×C₁₉	—	2	16	no	—
147	C₂×C₄×C₁₉	—	2	8	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	8	no	—
152	C₂×C₄×C₁₉	—	2	16	no	—
153	C₂×C₄×C₁₉	—	2	8	no	—
154	C₂×C₄×C₁₉	—	4	32	no	—
155	C₂×C₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	—	4	16	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	1	no	—
162	C₂×C₄×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	4	2	no	—
164	C₂×C₄×C₁₉	#120	1	2	yes	—
165	C₂×C₄×C₁₉	#123	1	4	yes	—
166	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
168	C₈×C₁₉	—	4	4	no	—
169	C₂³×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
170	C₂×#480	C₂×C₁₉	1	2	yes	complemented
171	#2847	C₂×C₁₉	1	1	yes	characteristic
172	#1874	C₂×C₁₉	1	4	yes	complemented
173	#1852	C₂×C₁₉	1	4	yes	complemented
174	#1823	C₂×C₁₉	1	2	yes	complemented
175	#1779	C₂×C₁₉	1	1	yes	characteristic, complemented
176	C₂²×C₁₉	—	2	32	no	—
177	C₂²×C₁₉	—	2	4	no	—
178	C₂²×C₁₉	—	2	4	no	—
179	C₂²×C₁₉	—	2	4	no	—
180	C₂²×C₁₉	—	2	4	no	—
181	C₂²×C₁₉	—	2	4	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	2	4	no	—
185	C₂²×C₁₉	—	2	2	no	—
186	C₂²×C₁₉	—	2	4	no	—
187	C₂²×C₁₉	—	8	2	no	—
188	C₂²×C₁₉	—	8	2	no	—
189	C₂²×C₁₉	—	8	1	no	—
190	C₂²×C₁₉	—	8	1	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	#447	1	4	yes	—
193	C₂²×C₁₉	#480	1	8	yes	complemented
194	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
195	C₂²×C₁₉	C₂×#123	1	2	yes	—
196	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
197	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂²×C₁₉	C₂×#137	1	2	yes	—
199	C₄×C₁₉	—	2	2	no	—
200	C₄×C₁₉	—	2	4	no	—
201	C₄×C₁₉	—	4	8	no	—
202	C₄×C₁₉	—	8	2	no	—
203	C₄×C₁₉	—	8	1	no	—
204	C₄×C₁₉	#525	1	4	yes	—
205	C₂⁴×C₄	—	2	1	no	—
206	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
207	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
208	C₂×#121	C₂²×C₁₉	1	2	yes	—
209	C₂×#120	—	2	1	no	—
210	C₂²×C₄⋊C₄	—	2	1	no	—
211	C₂²×C₄⋊C₄	—	2	2	no	—
212	C₂²×C₄⋊C₄	—	2	8	no	—
213	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
215	#480	—	2	8	no	—
216	C₂×#107	C₂²×C₁₉	1	4	yes	complemented
217	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
218	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
219	C₂×C₂²⋊C₈	C₂²×C₁₉	1	4	yes	—
220	#386	—	2	2	no	—
221	#386	—	2	1	no	—
222	#380	C₂²×C₁₉	1	1	yes	characteristic
223	#380	C₂²×C₁₉	1	2	yes	—
224	#340	C₂²×C₁₉	1	8	yes	complemented
225	C₂×C₁₉	—	2	4	no	—
226	C₂×C₁₉	—	2	8	no	—
227	C₂×C₁₉	—	16	1	no	—
228	C₂×C₁₉	#2849	1	1	yes	characteristic
229	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
230	C₂×C₁₉	#3004	1	1	yes	characteristic
231	C₂×C₁₉	C₂×#480	1	2	yes	—
232	C₂×C₁₉	#3092	1	2	yes	—
233	C₂⁵	D₄×C₁₉	1	1	yes	characteristic
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
237	C₂³×C₄	—	2	4	no	—
238	C₂³×C₄	—	2	8	no	—
239	C₂³×C₄	—	2	8	no	—
240	C₂³×C₄	—	2	4	no	—
241	C₂³×C₄	—	2	2	no	—
242	C₂³×C₄	—	4	4	no	—
243	C₂³×C₄	—	4	4	no	—
244	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₁₉	1	2	yes	—
246	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
249	#121	—	2	4	no	—
250	#121	—	2	8	no	—
251	#120	—	4	4	no	—
252	C₂×C₄⋊C₄	—	2	8	no	—
253	C₂×C₄⋊C₄	—	2	16	no	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	16	no	—
258	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	complemented
259	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	#107	—	2	8	no	—
267	#102	—	2	8	no	—
268	C₂²⋊C₈	—	2	4	no	—
269	C₂²⋊C₈	—	2	8	no	—
270	#95	—	2	1	no	—
271	#95	—	2	2	no	—
272	C₁₉	#32978	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁴	—	2	2	no	—
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	—	2	1	no	—
278	C₂⁴	D₈×C₁₉	1	4	yes	—
279	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
280	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	—	4	4	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	4	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂²×C₄	—	2	32	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	16	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	32	no	—
304	C₂²×C₄	—	4	8	no	—
305	C₂²×C₄	—	4	8	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
311	C₂²×C₄	#41×C₁₉	1	8	yes	—
312	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	8	no	—
315	C₄⋊C₄	—	2	16	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	C₂×D₄×C₁₉	1	8	yes	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂³	—	2	8	no	—
326	C₂³	—	2	8	no	—
327	C₂³	—	2	16	no	—
328	C₂³	—	2	8	no	—
329	C₂³	—	2	16	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	2	no	—
341	C₂³	C₁₉×#120	1	2	yes	—
342	C₂³	C₁₉×#123	1	4	yes	—
343	C₂³	C₂×D₈×C₁₉	1	2	yes	—
344	C₂³	C₂×D₈×C₁₉	1	4	yes	—
345	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
346	C₂³	C₁₉×#137	1	4	yes	—
347	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
348	D₄	—	4	4	no	—
349	D₄	—	8	4	no	—
350	D₄	—	8	8	no	—
351	C₂×C₄	—	2	16	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	16	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	4	32	no	—
360	C₂×C₄	—	4	16	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	C₁₉×#120	1	2	yes	—
370	C₂×C₄	C₁₉×#123	1	4	yes	—
371	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
372	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
373	C₈	—	4	4	no	—
374	C₂²	—	2	32	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	8	1	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	1	no	—
390	C₂²	C₁₉×#447	1	4	yes	—
391	C₂²	C₁₉×#480	1	8	yes	complemented
392	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
393	C₂²	C₂×C₁₉×#123	1	2	yes	—
394	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
395	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
396	C₂²	C₂×C₁₉×#137	1	2	yes	—
397	C₄	—	2	2	no	—
398	C₄	—	2	4	no	—
399	C₄	—	4	8	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	2	no	—
402	C₄	C₁₉×#525	1	4	yes	—
403	C₂	—	2	4	no	—
404	C₂	—	2	8	no	—
405	C₂	—	16	1	no	—
406	C₂	C₁₉×#2849	1	1	yes	characteristic
407	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
408	C₂	C₁₉×#3004	1	1	yes	characteristic
409	C₂	C₂×C₁₉×#480	1	2	yes	—
410	C₂	C₁₉×#3092	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2847	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂⁴×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄⋊C₄×C₁₉	C₂	semidirect
2. C₂×C₁₉×#480	C₂	semidirect
4. C₁₉×#1874	C₂	semidirect
5. C₁₉×#1852	C₂	semidirect
6. C₁₉×#1823	C₂	semidirect
7. C₁₉×#1779	C₂	semidirect
19. C₂×C₁₉×#107	C₂²	semidirect
20. C₂×C₁₉×#102	C₂²	semidirect
27. C₁₉×#340	C₂²	semidirect
53. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
119. #32978	C₁₉	direct (N × H)
169. C₂³×C₄⋊C₄	C₂×C₁₉	semidirect
170. C₂×#480	C₂×C₁₉	semidirect
172. #1874	C₂×C₁₉	semidirect
173. #1852	C₂×C₁₉	semidirect
174. #1823	C₂×C₁₉	semidirect
175. #1779	C₂×C₁₉	semidirect
193. C₂²×C₁₉	#480	semidirect
216. C₂×#107	C₂²×C₁₉	semidirect
217. C₂×#102	C₂²×C₁₉	semidirect
224. #340	C₂²×C₁₉	semidirect
258. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
272. C₁₉	#32978	direct (N × H)
391. C₂²	C₁₉×#480	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₁₉	2
C₂×C₁₉×#480	2
C₁₉×#2847	2
C₁₉×#1874	2
C₁₉×#1852	2
C₁₉×#1823	2
C₁₉×#1779	2
#32978	19

Subgroups — C19×#32978 #18038937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32978 #18038937