Subgroups — C₁₉×#34578 #18040537

Order 4864.

2002 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2667	C₂	1	4	yes	maximal, complemented
2	C₁₉×#2665	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2659	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2646	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2626	C₂	1	4	yes	maximal
6	C₁₉×#2396	C₂	1	8	yes	maximal, complemented
7	C₄×C₁₉×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
8	C₁₉×#2280	C₂	1	2	yes	maximal
9	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	4	yes	—
12	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	complemented
13	C₂×C₁₉×#117	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#400	C₂²	1	8	yes	complemented
17	C₁₉×#399	C₂²	1	8	yes	—
18	C₁₉×#398	C₂²	1	8	yes	complemented
19	C₁₉×#398	C₂²	1	8	yes	complemented
20	C₁₉×#396	C₂²	1	8	yes	—
21	C₁₉×#396	C₂²	1	8	yes	—
22	C₁₉×#395	C₂²	1	8	yes	complemented
23	C₁₉×#393	C₂²	1	8	yes	—
24	C₁₉×#391	C₂²	1	4	yes	complemented
25	C₁₉×#389	C₂²	1	4	yes	complemented
26	C₁₉×#387	C₂²	1	8	yes	complemented
27	C₁₉×#385	C₂²	1	8	yes	—
28	C₁₉×#381	C₂²	1	4	yes	—
29	C₁₉×#380	C₂²	1	4	yes	—
30	C₁₉×#380	C₂²	1	4	yes	—
31	C₁₉×#380	C₂²	1	2	yes	—
32	C₁₉×#380	C₂²	1	2	yes	—
33	C₁₉×#379	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	complemented
35	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
36	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
37	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
38	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
39	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
40	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
41	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
42	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
44	C₂³×C₄×C₁₉	—	4	4	no	—
45	C₂³×C₄×C₁₉	Q₈	1	8	yes	complemented
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
52	C₁₉×C₂²⋊Q₈	—	2	16	no	—
53	C₄×Q₈×C₁₉	—	4	8	no	—
54	C₁₉×#117	—	4	8	no	—
55	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
56	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
65	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
66	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
69	C₂×C₄²×C₁₉	—	4	4	no	—
70	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
72	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
73	C₁₉×#95	C₂³	1	4	yes	—
74	C₁₉×#95	C₂³	1	4	yes	—
75	C₁₉×#95	C₂³	1	4	yes	—
76	C₁₉×#95	C₂³	1	4	yes	—
77	C₁₉×#95	C₂³	1	8	yes	—
78	C₁₉×#95	C₂³	1	8	yes	—
79	C₁₉×#95	C₂³	1	8	yes	—
80	C₁₉×#95	C₂³	1	8	yes	—
81	C₂⁴×C₁₉	—	2	4	no	—
82	C₂⁴×C₁₉	—	4	2	no	—
83	C₂⁴×C₁₉	—	4	1	no	—
84	C₂⁴×C₁₉	—	4	1	no	—
85	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
86	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
87	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
88	C₂×Q₈×C₁₉	—	2	8	no	—
89	C₂×Q₈×C₁₉	—	4	4	no	—
90	C₂×Q₈×C₁₉	—	4	4	no	—
91	C₂²×C₄×C₁₉	—	2	4	no	—
92	C₂²×C₄×C₁₉	—	2	8	no	—
93	C₂²×C₄×C₁₉	—	2	4	no	—
94	C₂²×C₄×C₁₉	—	4	16	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	4	no	—
98	C₂²×C₄×C₁₉	—	4	2	no	—
99	C₂²×C₄×C₁₉	—	4	2	no	—
100	C₂²×C₄×C₁₉	—	4	2	no	—
101	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
102	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
103	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
104	C₂²×C₄×C₁₉	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₁₉	#41	1	8	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
113	C₄⋊C₄×C₁₉	—	2	8	no	—
114	C₄⋊C₄×C₁₉	—	2	16	no	—
115	C₄⋊C₄×C₁₉	—	4	4	no	—
116	C₄⋊C₄×C₁₉	—	4	8	no	—
117	C₄⋊C₄×C₁₉	—	4	4	no	—
118	C₄⋊C₄×C₁₉	—	4	4	no	—
119	C₄⋊C₄×C₁₉	—	4	4	no	—
120	C₄⋊C₄×C₁₉	—	4	8	no	—
121	C₂²⋊C₄×C₁₉	—	2	16	no	—
122	C₂²⋊C₄×C₁₉	—	2	16	no	—
123	C₂²⋊C₄×C₁₉	—	4	4	no	—
124	C₂²⋊C₄×C₁₉	—	4	4	no	—
125	C₂²⋊C₄×C₁₉	—	4	8	no	—
126	C₄²×C₁₉	—	2	8	no	—
127	C₄²×C₁₉	—	2	16	no	—
128	C₄²×C₁₉	—	4	4	no	—
129	#34578	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	2	1	no	—
132	C₂³×C₁₉	—	2	1	no	—
133	C₂³×C₁₉	—	2	8	no	—
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	2	4	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	4	4	no	—
139	C₂³×C₁₉	—	4	4	no	—
140	C₂³×C₁₉	—	4	8	no	—
141	C₂³×C₁₉	—	4	8	no	—
142	C₂³×C₁₉	C₂²×Q₈	1	4	yes	—
143	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
144	C₂³×C₁₉	C₂×#41	1	4	yes	—
145	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
146	Q₈×C₁₉	—	4	16	no	—
147	C₂×C₄×C₁₉	—	2	4	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	2	4	no	—
151	C₂×C₄×C₁₉	—	2	8	no	—
152	C₂×C₄×C₁₉	—	2	16	no	—
153	C₂×C₄×C₁₉	—	2	4	no	—
154	C₂×C₄×C₁₉	—	2	8	no	—
155	C₂×C₄×C₁₉	—	2	8	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	8	no	—
158	C₂×C₄×C₁₉	—	2	8	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	4	4	no	—
163	C₂×C₄×C₁₉	—	4	8	no	—
164	C₂×C₄×C₁₉	—	4	8	no	—
165	C₂×C₄×C₁₉	—	4	8	no	—
166	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
167	C₂×C₄×C₁₉	C₂²×Q₈	1	4	yes	—
168	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
169	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
170	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
171	#2667	C₂×C₁₉	1	4	yes	complemented
172	#2665	C₂×C₁₉	1	4	yes	complemented
173	#2659	C₂×C₁₉	1	2	yes	complemented
174	#2646	C₂×C₁₉	1	2	yes	complemented
175	#2626	C₂×C₁₉	1	4	yes	—
176	#2396	C₂×C₁₉	1	8	yes	complemented
177	C₄×C₂²⋊Q₈	C₂×C₁₉	1	4	yes	complemented
178	#2280	C₂×C₁₉	1	2	yes	—
179	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	4	no	—
183	C₂²×C₁₉	—	2	4	no	—
184	C₂²×C₁₉	—	2	4	no	—
185	C₂²×C₁₉	—	2	4	no	—
186	C₂²×C₁₉	—	2	4	no	—
187	C₂²×C₁₉	—	4	16	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	4	4	no	—
190	C₂²×C₁₉	#533	1	4	yes	—
191	C₂²×C₁₉	C₂³×Q₈	1	1	yes	characteristic
192	C₂²×C₁₉	C₂²×#41	1	2	yes	—
193	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
194	C₂²×C₁₉	#585	1	1	yes	characteristic
195	C₂²×C₁₉	#585	1	1	yes	characteristic
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	4	no	—
198	C₄×C₁₉	—	2	8	no	—
199	C₄×C₁₉	—	4	8	no	—
200	C₄×C₁₉	—	4	8	no	—
201	C₄×C₁₉	—	4	4	no	—
202	C₄×C₁₉	#543	1	4	yes	—
203	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
204	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	4	yes	—
205	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	complemented
206	C₂×#117	C₂²×C₁₉	1	4	yes	—
207	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
208	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
209	#400	C₂²×C₁₉	1	8	yes	complemented
210	#399	C₂²×C₁₉	1	8	yes	—
211	#398	C₂²×C₁₉	1	8	yes	complemented
212	#398	C₂²×C₁₉	1	8	yes	complemented
213	#396	C₂²×C₁₉	1	8	yes	—
214	#396	C₂²×C₁₉	1	8	yes	—
215	#395	C₂²×C₁₉	1	8	yes	complemented
216	#393	C₂²×C₁₉	1	8	yes	—
217	#391	C₂²×C₁₉	1	4	yes	complemented
218	#389	C₂²×C₁₉	1	4	yes	complemented
219	#387	C₂²×C₁₉	1	8	yes	complemented
220	#385	C₂²×C₁₉	1	8	yes	—
221	#381	C₂²×C₁₉	1	4	yes	—
222	#380	C₂²×C₁₉	1	4	yes	—
223	#380	C₂²×C₁₉	1	4	yes	—
224	#380	C₂²×C₁₉	1	2	yes	—
225	#380	C₂²×C₁₉	1	2	yes	—
226	#379	C₂²×C₁₉	1	4	yes	—
227	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	complemented
228	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
229	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
230	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
231	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
232	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
233	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
234	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₁₉	—	2	4	no	—
236	C₂×C₁₉	—	4	4	no	—
237	C₂×C₁₉	C₂×#533	1	1	yes	characteristic
238	C₂×C₁₉	C₂×#543	1	1	yes	characteristic
239	C₂×C₁₉	#3458	1	1	yes	characteristic
240	C₂×C₁₉	#3459	1	2	yes	—
241	C₂×C₁₉	#3460	1	2	yes	—
242	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
244	C₂³×C₄	—	4	4	no	—
245	C₂³×C₄	Q₈×C₁₉	1	8	yes	complemented
246	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
247	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
249	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
251	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
252	C₂²⋊Q₈	—	2	16	no	—
253	C₄×Q₈	—	4	8	no	—
254	#117	—	4	8	no	—
255	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
259	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
261	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
263	C₂×C₂²⋊C₄	—	2	8	no	—
264	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
265	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
269	C₂×C₄²	—	4	4	no	—
270	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
271	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
272	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
273	#95	C₂³×C₁₉	1	4	yes	—
274	#95	C₂³×C₁₉	1	4	yes	—
275	#95	C₂³×C₁₉	1	4	yes	—
276	#95	C₂³×C₁₉	1	4	yes	—
277	#95	C₂³×C₁₉	1	8	yes	—
278	#95	C₂³×C₁₉	1	8	yes	—
279	#95	C₂³×C₁₉	1	8	yes	—
280	#95	C₂³×C₁₉	1	8	yes	—
281	C₁₉	#34578	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	4	2	no	—
284	C₂⁴	—	4	1	no	—
285	C₂⁴	—	4	1	no	—
286	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
287	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
288	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
289	C₂×Q₈	—	2	8	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×Q₈	—	4	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	4	16	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
303	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
304	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
305	C₂²×C₄	C₂×Q₈×C₁₉	1	4	yes	—
306	C₂²×C₄	#41×C₁₉	1	8	yes	—
307	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
308	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
309	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
310	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
313	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	16	no	—
316	C₄⋊C₄	—	4	4	no	—
317	C₄⋊C₄	—	4	8	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	4	4	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	8	no	—
322	C₂²⋊C₄	—	2	16	no	—
323	C₂²⋊C₄	—	2	16	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₂²⋊C₄	—	4	8	no	—
327	C₄²	—	2	8	no	—
328	C₄²	—	2	16	no	—
329	C₄²	—	4	4	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	8	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	8	no	—
341	C₂³	—	4	8	no	—
342	C₂³	C₂²×Q₈×C₁₉	1	4	yes	—
343	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
344	C₂³	C₂×#41×C₁₉	1	4	yes	—
345	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
346	Q₈	—	4	16	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	16	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
367	C₂×C₄	C₂²×Q₈×C₁₉	1	4	yes	—
368	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
369	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
370	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	4	16	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	C₁₉×#533	1	4	yes	—
382	C₂²	C₂³×Q₈×C₁₉	1	1	yes	characteristic
383	C₂²	C₂²×#41×C₁₉	1	2	yes	—
384	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
385	C₂²	C₁₉×#585	1	1	yes	characteristic
386	C₂²	C₁₉×#585	1	1	yes	characteristic
387	C₄	—	2	2	no	—
388	C₄	—	2	4	no	—
389	C₄	—	2	8	no	—
390	C₄	—	4	8	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	8	no	—
393	C₄	C₁₉×#543	1	4	yes	—
394	C₂	—	2	4	no	—
395	C₂	—	4	4	no	—
396	C₂	C₂×C₁₉×#533	1	1	yes	characteristic
397	C₂	C₂×C₁₉×#543	1	1	yes	characteristic
398	C₂	C₁₉×#3458	1	1	yes	characteristic
399	C₂	C₁₉×#3459	1	2	yes	—
400	C₂	C₁₉×#3460	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2667	C₂	semidirect
2. C₁₉×#2665	C₂	semidirect
3. C₁₉×#2659	C₂	semidirect
4. C₁₉×#2646	C₂	semidirect
6. C₁₉×#2396	C₂	semidirect
7. C₄×C₁₉×C₂²⋊Q₈	C₂	semidirect
12. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
16. C₁₉×#400	C₂²	semidirect
18. C₁₉×#398	C₂²	semidirect
19. C₁₉×#398	C₂²	semidirect
22. C₁₉×#395	C₂²	semidirect
24. C₁₉×#391	C₂²	semidirect
25. C₁₉×#389	C₂²	semidirect
26. C₁₉×#387	C₂²	semidirect
34. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
35. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
45. C₂³×C₄×C₁₉	Q₈	semidirect
129. #34578	C₁₉	direct (N × H)
171. #2667	C₂×C₁₉	semidirect
172. #2665	C₂×C₁₉	semidirect
173. #2659	C₂×C₁₉	semidirect
174. #2646	C₂×C₁₉	semidirect
176. #2396	C₂×C₁₉	semidirect
177. C₄×C₂²⋊Q₈	C₂×C₁₉	semidirect
205. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
209. #400	C₂²×C₁₉	semidirect
211. #398	C₂²×C₁₉	semidirect
212. #398	C₂²×C₁₉	semidirect
215. #395	C₂²×C₁₉	semidirect
217. #391	C₂²×C₁₉	semidirect
218. #389	C₂²×C₁₉	semidirect
219. #387	C₂²×C₁₉	semidirect
227. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
228. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
245. C₂³×C₄	Q₈×C₁₉	semidirect
281. C₁₉	#34578	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×#2667	2
C₁₉×#2665	2
C₁₉×#2659	2
C₁₉×#2646	2
C₁₉×#2626	2
C₁₉×#2396	2
C₄×C₁₉×C₂²⋊Q₈	2
C₁₉×#2280	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
#34578	19

Subgroups — C19×#34578 #18040537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34578 #18040537