Subgroups — C₁₉×#14127 #18020086

Order 4864.

4046 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊C₄×C₁₉	C₂	1	2	yes	maximal
2	C₂×C₁₉×#385	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#379	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1439	C₂	1	4	yes	maximal, complemented
5	C₁₉×C₂²⋊#95	C₂	1	4	yes	maximal, complemented
6	C₂⁶×C₁₉	C₂²	1	1	yes	characteristic
7	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	complemented
10	C₂²×C₂²⋊C₄×C₁₉	—	2	8	no	—
11	C₂²×C₂²⋊C₄×C₁₉	—	2	16	no	—
12	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
13	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
15	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
16	C₁₉×#385	—	2	16	no	—
17	C₁₉×#379	C₄	1	8	yes	complemented
18	C₂×C₁₉×#95	C₂²	1	8	yes	complemented
19	C₂×C₁₉×#95	C₂²	1	4	yes	complemented
20	C₂⁵×C₁₉	—	2	8	no	—
21	C₂⁵×C₁₉	—	2	8	no	—
22	C₂⁵×C₁₉	—	4	2	no	—
23	C₂⁵×C₁₉	—	4	2	no	—
24	C₂⁵×C₁₉	C₂×C₄	1	4	yes	—
25	C₂⁵×C₁₉	D₄	1	4	yes	—
26	C₂⁵×C₁₉	Q₈	1	4	yes	—
27	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
28	C₂⁵×C₁₉	C₂³	1	2	yes	—
29	C₂³×C₄×C₁₉	—	2	4	no	—
30	C₂³×C₄×C₁₉	—	2	4	no	—
31	C₂³×C₄×C₁₉	—	2	8	no	—
32	C₂³×C₄×C₁₉	—	2	8	no	—
33	C₂³×C₄×C₁₉	—	2	8	no	—
34	C₂³×C₄×C₁₉	—	2	8	no	—
35	C₂³×C₄×C₁₉	—	4	4	no	—
36	C₂³×C₄×C₁₉	—	4	4	no	—
37	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
38	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
40	C₂×C₄⋊C₄×C₁₉	—	2	16	no	—
41	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	64	no	—
43	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
44	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
45	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
46	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
47	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
49	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
50	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
51	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
52	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	16	yes	complemented
53	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
54	C₂×C₂²⋊C₄×C₁₉	D₄	1	16	yes	—
55	C₁₉×#95	—	2	16	no	—
56	C₁₉×#95	—	4	4	no	—
57	C₂⁴×C₁₉	—	2	4	no	—
58	C₂⁴×C₁₉	—	2	4	no	—
59	C₂⁴×C₁₉	—	2	4	no	—
60	C₂⁴×C₁₉	—	2	4	no	—
61	C₂⁴×C₁₉	—	2	32	no	—
62	C₂⁴×C₁₉	—	2	16	no	—
63	C₂⁴×C₁₉	—	2	32	no	—
64	C₂⁴×C₁₉	—	2	16	no	—
65	C₂⁴×C₁₉	—	2	4	no	—
66	C₂⁴×C₁₉	—	2	4	no	—
67	C₂⁴×C₁₉	—	2	2	no	—
68	C₂⁴×C₁₉	—	2	2	no	—
69	C₂⁴×C₁₉	—	4	8	no	—
70	C₂⁴×C₁₉	—	4	4	no	—
71	C₂⁴×C₁₉	—	4	4	no	—
72	C₂⁴×C₁₉	—	4	8	no	—
73	C₂⁴×C₁₉	—	4	16	no	—
74	C₂⁴×C₁₉	—	4	32	no	—
75	C₂⁴×C₁₉	—	4	16	no	—
76	C₂⁴×C₁₉	C₄⋊C₄	1	16	yes	complemented
77	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
78	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
79	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
80	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
81	C₂⁴×C₁₉	C₂×D₄	1	8	yes	—
82	C₂⁴×C₁₉	C₂×Q₈	1	2	yes	—
83	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
84	C₂⁴×C₁₉	#41	1	8	yes	—
85	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	—	2	16	no	—
87	C₂²×C₄×C₁₉	—	2	16	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	8	no	—
93	C₂²×C₄×C₁₉	—	2	8	no	—
94	C₂²×C₄×C₁₉	—	2	8	no	—
95	C₂²×C₄×C₁₉	—	2	8	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	8	no	—
99	C₂²×C₄×C₁₉	—	2	8	no	—
100	C₂²×C₄×C₁₉	—	4	32	no	—
101	C₂²×C₄×C₁₉	—	4	32	no	—
102	C₂²×C₄×C₁₉	—	4	8	no	—
103	C₂²×C₄×C₁₉	—	4	8	no	—
104	C₂²×C₄×C₁₉	—	4	8	no	—
105	C₂²×C₄×C₁₉	—	4	8	no	—
106	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
107	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
109	C₄⋊C₄×C₁₉	—	4	16	no	—
110	C₂²⋊C₄×C₁₉	—	2	32	no	—
111	C₂²⋊C₄×C₁₉	—	2	32	no	—
112	C₂²⋊C₄×C₁₉	—	2	32	no	—
113	C₂²⋊C₄×C₁₉	—	4	8	no	—
114	#14127	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₁₉	—	2	8	no	—
116	C₂³×C₁₉	—	2	8	no	—
117	C₂³×C₁₉	—	2	4	no	—
118	C₂³×C₁₉	—	2	8	no	—
119	C₂³×C₁₉	—	2	4	no	—
120	C₂³×C₁₉	—	2	4	no	—
121	C₂³×C₁₉	—	2	4	no	—
122	C₂³×C₁₉	—	2	8	no	—
123	C₂³×C₁₉	—	2	16	no	—
124	C₂³×C₁₉	—	2	16	no	—
125	C₂³×C₁₉	—	2	16	no	—
126	C₂³×C₁₉	—	2	16	no	—
127	C₂³×C₁₉	—	2	8	no	—
128	C₂³×C₁₉	—	2	4	no	—
129	C₂³×C₁₉	—	2	4	no	—
130	C₂³×C₁₉	—	2	8	no	—
131	C₂³×C₁₉	—	2	4	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	2	64	no	—
136	C₂³×C₁₉	—	4	16	no	—
137	C₂³×C₁₉	—	4	64	no	—
138	C₂³×C₁₉	—	4	16	no	—
139	C₂³×C₁₉	—	4	32	no	—
140	C₂³×C₁₉	—	4	64	no	—
141	C₂³×C₁₉	—	4	16	no	—
142	C₂³×C₁₉	—	4	4	no	—
143	C₂³×C₁₉	—	4	8	no	—
144	C₂³×C₁₉	—	4	4	no	—
145	C₂³×C₁₉	C₂×C₄⋊C₄	1	4	yes	—
146	C₂³×C₁₉	C₂×C₄⋊C₄	1	8	yes	—
147	C₂³×C₁₉	C₄×D₄	1	16	yes	—
148	C₂³×C₁₉	#120	1	8	yes	—
149	C₂³×C₁₉	C₂²⋊Q₈	1	16	yes	—
150	C₂³×C₁₉	#123	1	8	yes	—
151	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
152	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
153	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
154	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
155	C₂³×C₁₉	C₂×#41	1	4	yes	—
156	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
157	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
158	C₂×C₄×C₁₉	—	2	16	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	2	8	no	—
162	C₂×C₄×C₁₉	—	2	16	no	—
163	C₂×C₄×C₁₉	—	2	16	no	—
164	C₂×C₄×C₁₉	—	4	32	no	—
165	C₂×C₄×C₁₉	—	4	32	no	—
166	C₂×C₄×C₁₉	—	4	4	no	—
167	C₂×C₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	4	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	—	4	4	no	—
171	C₂×C₄×C₁₉	—	4	8	no	—
172	C₂×C₄×C₁₉	—	4	8	no	—
173	C₂×C₄×C₁₉	—	4	8	no	—
174	C₂×C₄×C₁₉	—	4	4	no	—
175	C₂³×C₂²⋊C₄	C₂×C₁₉	1	2	yes	—
176	C₂×#385	C₂×C₁₉	1	4	yes	complemented
177	C₂×#379	C₂×C₁₉	1	1	yes	characteristic
178	#1439	C₂×C₁₉	1	4	yes	complemented
179	C₂²⋊#95	C₂×C₁₉	1	4	yes	complemented
180	C₂²×C₁₉	—	2	8	no	—
181	C₂²×C₁₉	—	2	32	no	—
182	C₂²×C₁₉	—	2	8	no	—
183	C₂²×C₁₉	—	2	8	no	—
184	C₂²×C₁₉	—	2	8	no	—
185	C₂²×C₁₉	—	2	32	no	—
186	C₂²×C₁₉	—	2	8	no	—
187	C₂²×C₁₉	—	2	8	no	—
188	C₂²×C₁₉	—	2	4	no	—
189	C₂²×C₁₉	—	2	8	no	—
190	C₂²×C₁₉	—	4	64	no	—
191	C₂²×C₁₉	—	4	8	no	—
192	C₂²×C₁₉	—	4	2	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	4	8	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	#385	1	16	yes	complemented
197	C₂²×C₁₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
198	C₂²×C₁₉	C₂×C₄×D₄	1	4	yes	—
199	C₂²×C₁₉	#518	1	2	yes	—
200	C₂²×C₁₉	C₂×#120	1	2	yes	—
201	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	4	yes	—
202	C₂²×C₁₉	C₂×#123	1	2	yes	—
203	C₂²×C₁₉	#534	1	1	yes	characteristic
204	C₂²×C₁₉	#534	1	1	yes	characteristic
205	C₂²×C₁₉	#543	1	2	yes	—
206	C₂²×C₁₉	D₄²	1	4	yes	—
207	C₂²×C₁₉	#546	1	8	yes	—
208	C₂²×C₁₉	#551	1	4	yes	—
209	C₄×C₁₉	—	4	8	no	—
210	C₄×C₁₉	—	4	8	no	—
211	C₄×C₁₉	—	4	8	no	—
212	C₂⁶	C₂²×C₁₉	1	1	yes	characteristic
213	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
214	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	complemented
216	C₂²×C₂²⋊C₄	—	2	8	no	—
217	C₂²×C₂²⋊C₄	—	2	16	no	—
218	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
219	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
220	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
221	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
222	#385	—	2	16	no	—
223	#379	C₄×C₁₉	1	8	yes	complemented
224	C₂×#95	C₂²×C₁₉	1	8	yes	complemented
225	C₂×#95	C₂²×C₁₉	1	4	yes	complemented
226	C₂×C₁₉	—	2	16	no	—
227	C₂×C₁₉	—	4	4	no	—
228	C₂×C₁₉	C₂×#385	1	2	yes	—
229	C₂×C₁₉	#2315	1	1	yes	characteristic
230	C₂×C₁₉	#2358	1	4	yes	—
231	C₂×C₁₉	#2403	1	1	yes	characteristic
232	C₂×C₁₉	#2405	1	2	yes	—
233	C₂×C₁₉	#2437	1	4	yes	—
234	C₂×C₁₉	#2483	1	1	yes	characteristic
235	C₂⁵	—	2	8	no	—
236	C₂⁵	—	2	8	no	—
237	C₂⁵	—	4	2	no	—
238	C₂⁵	—	4	2	no	—
239	C₂⁵	C₂×C₄×C₁₉	1	4	yes	—
240	C₂⁵	D₄×C₁₉	1	4	yes	—
241	C₂⁵	Q₈×C₁₉	1	4	yes	—
242	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
243	C₂⁵	C₂³×C₁₉	1	2	yes	—
244	C₂³×C₄	—	2	4	no	—
245	C₂³×C₄	—	2	4	no	—
246	C₂³×C₄	—	2	8	no	—
247	C₂³×C₄	—	2	8	no	—
248	C₂³×C₄	—	2	8	no	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	—	4	4	no	—
251	C₂³×C₄	—	4	4	no	—
252	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
253	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
254	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
255	C₂×C₄⋊C₄	—	2	16	no	—
256	C₂×C₄⋊C₄	—	4	4	no	—
257	C₂×C₂²⋊C₄	—	2	64	no	—
258	C₂×C₂²⋊C₄	—	2	8	no	—
259	C₂×C₂²⋊C₄	—	2	8	no	—
260	C₂×C₂²⋊C₄	—	2	8	no	—
261	C₂×C₂²⋊C₄	—	2	8	no	—
262	C₂×C₂²⋊C₄	—	2	8	no	—
263	C₂×C₂²⋊C₄	—	2	8	no	—
264	C₂×C₂²⋊C₄	—	2	8	no	—
265	C₂×C₂²⋊C₄	—	4	2	no	—
266	C₂×C₂²⋊C₄	—	4	2	no	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	16	yes	complemented
268	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
269	C₂×C₂²⋊C₄	D₄×C₁₉	1	16	yes	—
270	#95	—	2	16	no	—
271	#95	—	4	4	no	—
272	C₁₉	#14127	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁴	—	2	4	no	—
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	4	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	—	2	32	no	—
278	C₂⁴	—	2	16	no	—
279	C₂⁴	—	2	32	no	—
280	C₂⁴	—	2	16	no	—
281	C₂⁴	—	2	4	no	—
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	2	2	no	—
284	C₂⁴	—	2	2	no	—
285	C₂⁴	—	4	8	no	—
286	C₂⁴	—	4	4	no	—
287	C₂⁴	—	4	4	no	—
288	C₂⁴	—	4	8	no	—
289	C₂⁴	—	4	16	no	—
290	C₂⁴	—	4	32	no	—
291	C₂⁴	—	4	16	no	—
292	C₂⁴	C₄⋊C₄×C₁₉	1	16	yes	complemented
293	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
294	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
295	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
296	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
297	C₂⁴	C₂×D₄×C₁₉	1	8	yes	—
298	C₂⁴	C₂×Q₈×C₁₉	1	2	yes	—
299	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
300	C₂⁴	#41×C₁₉	1	8	yes	—
301	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
302	C₂²×C₄	—	2	16	no	—
303	C₂²×C₄	—	2	16	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	4	32	no	—
317	C₂²×C₄	—	4	32	no	—
318	C₂²×C₄	—	4	8	no	—
319	C₂²×C₄	—	4	8	no	—
320	C₂²×C₄	—	4	8	no	—
321	C₂²×C₄	—	4	8	no	—
322	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
323	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
324	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
325	C₄⋊C₄	—	4	16	no	—
326	C₂²⋊C₄	—	2	32	no	—
327	C₂²⋊C₄	—	2	32	no	—
328	C₂²⋊C₄	—	2	32	no	—
329	C₂²⋊C₄	—	4	8	no	—
330	C₂³	—	2	8	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	8	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	8	no	—
338	C₂³	—	2	16	no	—
339	C₂³	—	2	16	no	—
340	C₂³	—	2	16	no	—
341	C₂³	—	2	16	no	—
342	C₂³	—	2	64	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	2	8	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	4	16	no	—
352	C₂³	—	4	16	no	—
353	C₂³	—	4	32	no	—
354	C₂³	—	4	64	no	—
355	C₂³	—	4	16	no	—
356	C₂³	—	4	64	no	—
357	C₂³	—	4	4	no	—
358	C₂³	—	4	8	no	—
359	C₂³	—	4	4	no	—
360	C₂³	C₂×C₄⋊C₄×C₁₉	1	4	yes	—
361	C₂³	C₂×C₄⋊C₄×C₁₉	1	8	yes	—
362	C₂³	C₄×D₄×C₁₉	1	16	yes	—
363	C₂³	C₁₉×#120	1	8	yes	—
364	C₂³	C₁₉×C₂²⋊Q₈	1	16	yes	—
365	C₂³	C₁₉×#123	1	8	yes	—
366	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
367	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
368	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
369	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
370	C₂³	C₂×#41×C₁₉	1	4	yes	—
371	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
372	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
373	C₂×C₄	—	2	16	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	16	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	4	32	no	—
380	C₂×C₄	—	4	32	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	8	no	—
392	C₂²	—	2	8	no	—
393	C₂²	—	2	32	no	—
394	C₂²	—	2	8	no	—
395	C₂²	—	2	8	no	—
396	C₂²	—	2	8	no	—
397	C₂²	—	2	32	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	4	64	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	8	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	8	no	—
406	C₂²	C₁₉×#385	1	16	yes	complemented
407	C₂²	C₂²×C₄⋊C₄×C₁₉	1	1	yes	characteristic
408	C₂²	C₂×C₄×D₄×C₁₉	1	4	yes	—
409	C₂²	C₁₉×#518	1	2	yes	—
410	C₂²	C₂×C₁₉×#120	1	2	yes	—
411	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	4	yes	—
412	C₂²	C₂×C₁₉×#123	1	2	yes	—
413	C₂²	C₁₉×#534	1	1	yes	characteristic
414	C₂²	C₁₉×#534	1	1	yes	characteristic
415	C₂²	C₁₉×#543	1	2	yes	—
416	C₂²	D₄²×C₁₉	1	4	yes	—
417	C₂²	C₁₉×#546	1	8	yes	—
418	C₂²	C₁₉×#551	1	4	yes	—
419	C₄	—	4	8	no	—
420	C₄	—	4	8	no	—
421	C₄	—	4	8	no	—
422	C₂	—	2	16	no	—
423	C₂	—	4	4	no	—
424	C₂	C₂×C₁₉×#385	1	2	yes	—
425	C₂	C₁₉×#2315	1	1	yes	characteristic
426	C₂	C₁₉×#2358	1	4	yes	—
427	C₂	C₁₉×#2403	1	1	yes	characteristic
428	C₂	C₁₉×#2405	1	2	yes	—
429	C₂	C₁₉×#2437	1	4	yes	—
430	C₂	C₁₉×#2483	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁶×C₁₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#385	C₂	semidirect
4. C₁₉×#1439	C₂	semidirect
5. C₁₉×C₂²⋊#95	C₂	semidirect
9. C₂²×C₄⋊C₄×C₁₉	C₂²	semidirect
17. C₁₉×#379	C₄	semidirect
18. C₂×C₁₉×#95	C₂²	semidirect
19. C₂×C₁₉×#95	C₂²	semidirect
52. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
53. C₂×C₂²⋊C₄×C₁₉	C₂×C₄	semidirect
76. C₂⁴×C₁₉	C₄⋊C₄	semidirect
114. #14127	C₁₉	direct (N × H)
176. C₂×#385	C₂×C₁₉	semidirect
178. #1439	C₂×C₁₉	semidirect
179. C₂²⋊#95	C₂×C₁₉	semidirect
196. C₂²×C₁₉	#385	semidirect
215. C₂²×C₄⋊C₄	C₂²×C₁₉	semidirect
223. #379	C₄×C₁₉	semidirect
224. C₂×#95	C₂²×C₁₉	semidirect
225. C₂×#95	C₂²×C₁₉	semidirect
267. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
268. C₂×C₂²⋊C₄	C₂×C₄×C₁₉	semidirect
272. C₁₉	#14127	direct (N × H)
292. C₂⁴	C₄⋊C₄×C₁₉	semidirect
406. C₂²	C₁₉×#385	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊C₄×C₁₉	2
C₂×C₁₉×#385	2
C₂×C₁₉×#379	2
C₁₉×#1439	2
C₁₉×C₂²⋊#95	2
#14127	19

Subgroups — C19×#14127 #18020086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14127 #18020086