Subgroups — C₁₉×#32928 #18038887

Order 4864.

1618 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#458	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×B(4,𝔽₂)	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2534	C₂	1	3	yes	maximal, complemented
5	C₁₉×#1890	C₂	1	3	yes	maximal, complemented
6	C₁₉×#1889	C₂	1	3	yes	maximal, complemented
7	C₁₉×#1799	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
9	C₂×C₁₉×#123	C₂²	1	3	yes	—
10	C₂×C₁₉×#120	C₂²	1	3	yes	—
11	C₁₉×#520	—	2	3	no	—
12	C₁₉×#518	—	2	3	no	—
13	C₁₉×#518	C₂²	1	3	yes	—
14	C₄×#41×C₁₉	—	2	3	no	—
15	C₂×C₄×D₄×C₁₉	—	2	3	no	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	3	yes	—
17	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₁₉×#458	—	2	4	no	—
19	C₁₉×B(4,𝔽₂)	—	2	4	no	—
20	C₂×C₁₉×#99	C₂²	1	3	yes	—
21	C₂×C₁₉×#99	C₂²	1	3	yes	—
22	C₁₉×#396	—	2	3	no	—
23	C₁₉×#394	—	2	3	no	—
24	C₁₉×#388	—	2	3	no	—
25	C₁₉×#386	—	2	3	no	—
26	C₁₉×#381	C₂²	1	3	yes	complemented
27	C₁₉×#380	C₂²	1	3	yes	complemented
28	C₁₉×#379	C₂²	1	3	yes	complemented
29	C₁₉×#342	C₂²	1	6	yes	complemented
30	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
31	C₁₉×H(5,𝔽₂)	—	2	6	no	—
32	C₁₉×H(5,𝔽₂)	D₄	1	4	yes	—
33	C₂×#41×C₁₉	—	2	3	no	—
34	C₂²×D₄×C₁₉	—	2	3	no	—
35	C₂²×D₄×C₁₉	—	2	3	no	—
36	C₂²×D₄×C₁₉	C₂³	1	3	yes	—
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	D₄	1	3	yes	complemented
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₁₉×#123	—	2	6	no	—
42	C₁₉×#123	—	2	6	no	—
43	C₁₉×#120	—	2	6	no	—
44	C₁₉×#120	—	2	6	no	—
45	C₄×Q₈×C₁₉	—	2	1	no	—
46	C₄×Q₈×C₁₉	—	2	3	no	—
47	C₄×D₄×C₁₉	—	2	3	no	—
48	C₄×D₄×C₁₉	—	2	6	no	—
49	C₄×D₄×C₁₉	—	2	3	no	—
50	C₄×D₄×C₁₉	—	2	6	no	—
51	C₄×D₄×C₁₉	—	2	6	no	—
52	C₄×D₄×C₁₉	—	2	6	no	—
53	C₄×D₄×C₁₉	—	2	6	no	—
54	C₁₉×#117	—	2	6	no	—
55	C₁₉×#117	—	2	3	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	3	no	—
59	C₂×C₄⋊C₄×C₁₉	D₄	1	3	yes	complemented
60	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
61	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	3	no	—
68	C₂×C₂²⋊C₄×C₁₉	D₄	1	3	yes	complemented
69	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
70	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
71	C₂×C₂²⋊C₄×C₁₉	C₂³	1	3	yes	—
72	C₂×C₄²×C₁₉	—	2	3	no	—
73	C₂×C₄²×C₁₉	D₄	1	3	yes	complemented
74	C₁₉×#99	—	2	6	no	—
75	C₁₉×#99	—	2	6	no	—
76	C₁₉×#95	—	2	3	no	—
77	C₁₉×#95	—	2	3	no	—
78	C₁₉×#95	—	2	3	no	—
79	C₂⁴×C₁₉	—	2	1	no	—
80	C₂⁴×C₁₉	—	2	3	no	—
81	C₂⁴×C₁₉	—	2	1	no	—
82	C₂⁴×C₁₉	—	2	3	no	—
83	C₂⁴×C₁₉	—	4	2	no	—
84	C₂⁴×C₁₉	—	8	1	no	—
85	C₂⁴×C₁₉	C₂×D₄	1	3	yes	—
86	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
87	#41×C₁₉	—	2	12	no	—
88	#41×C₁₉	—	2	12	no	—
89	C₂×Q₈×C₁₉	—	2	1	no	—
90	C₂×D₄×C₁₉	—	2	3	no	—
91	C₂×D₄×C₁₉	—	2	12	no	—
92	C₂×D₄×C₁₉	—	2	12	no	—
93	C₂×D₄×C₁₉	—	2	6	no	—
94	C₂×D₄×C₁₉	—	2	6	no	—
95	C₂×D₄×C₁₉	—	4	6	no	—
96	C₂×D₄×C₁₉	—	4	6	no	—
97	C₂×D₄×C₁₉	—	8	3	no	—
98	C₂×D₄×C₁₉	C₂×D₄	1	6	yes	—
99	C₂×D₄×C₁₉	#41	1	6	yes	—
100	C₂²×C₄×C₁₉	—	2	3	no	—
101	C₂²×C₄×C₁₉	—	2	3	no	—
102	C₂²×C₄×C₁₉	—	2	3	no	—
103	C₂²×C₄×C₁₉	—	2	3	no	—
104	C₂²×C₄×C₁₉	—	2	3	no	—
105	C₂²×C₄×C₁₉	—	2	3	no	—
106	C₂²×C₄×C₁₉	—	2	3	no	—
107	C₂²×C₄×C₁₉	—	2	3	no	—
108	C₂²×C₄×C₁₉	—	2	1	no	—
109	C₂²×C₄×C₁₉	—	2	3	no	—
110	C₂²×C₄×C₁₉	—	8	1	no	—
111	C₂²×C₄×C₁₉	—	8	3	no	—
112	C₂²×C₄×C₁₉	—	8	2	no	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
115	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
116	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
117	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
118	C₄⋊C₄×C₁₉	—	2	3	no	—
119	C₄⋊C₄×C₁₉	—	2	3	no	—
120	C₄⋊C₄×C₁₉	—	2	6	no	—
121	C₄⋊C₄×C₁₉	—	4	6	no	—
122	C₄⋊C₄×C₁₉	—	8	3	no	—
123	C₂²⋊C₄×C₁₉	—	2	6	no	—
124	C₂²⋊C₄×C₁₉	—	2	6	no	—
125	C₂²⋊C₄×C₁₉	—	2	6	no	—
126	C₂²⋊C₄×C₁₉	—	2	3	no	—
127	C₂²⋊C₄×C₁₉	—	2	3	no	—
128	C₂²⋊C₄×C₁₉	—	2	3	no	—
129	C₂²⋊C₄×C₁₉	—	2	3	no	—
130	C₂²⋊C₄×C₁₉	—	4	6	no	—
131	C₂²⋊C₄×C₁₉	—	4	6	no	—
132	C₂²⋊C₄×C₁₉	—	4	1	no	—
133	C₂²⋊C₄×C₁₉	—	4	3	no	—
134	C₂²⋊C₄×C₁₉	—	4	6	no	—
135	C₂²⋊C₄×C₁₉	—	8	3	no	—
136	C₄²×C₁₉	—	2	6	no	—
137	C₄²×C₁₉	—	2	3	no	—
138	C₄²×C₁₉	—	2	3	no	—
139	#32928	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₉	—	2	4	no	—
141	C₂³×C₁₉	—	2	3	no	—
142	C₂³×C₁₉	—	2	3	no	—
143	C₂³×C₁₉	—	2	6	no	—
144	C₂³×C₁₉	—	4	1	no	—
145	C₂³×C₁₉	—	4	1	no	—
146	C₂³×C₁₉	—	4	3	no	—
147	C₂³×C₁₉	—	4	3	no	—
148	C₂³×C₁₉	—	4	3	no	—
149	C₂³×C₁₉	—	4	3	no	—
150	C₂³×C₁₉	—	4	3	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	3	no	—
153	C₂³×C₁₉	—	4	3	no	—
154	C₂³×C₁₉	—	8	2	no	—
155	C₂³×C₁₉	—	8	6	no	—
156	C₂³×C₁₉	—	8	1	no	—
157	C₂³×C₁₉	—	8	1	no	—
158	C₂³×C₁₉	#121	1	6	yes	—
159	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
160	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
161	C₂³×C₁₉	C₂×#41	1	3	yes	—
162	Q₈×C₁₉	—	2	4	no	—
163	D₄×C₁₉	—	2	12	no	—
164	D₄×C₁₉	—	2	12	no	—
165	D₄×C₁₉	—	2	12	no	—
166	D₄×C₁₉	—	8	12	no	—
167	C₂×C₄×C₁₉	—	2	12	no	—
168	C₂×C₄×C₁₉	—	2	3	no	—
169	C₂×C₄×C₁₉	—	2	3	no	—
170	C₂×C₄×C₁₉	—	2	3	no	—
171	C₂×C₄×C₁₉	—	2	3	no	—
172	C₂×C₄×C₁₉	—	4	3	no	—
173	C₂×C₄×C₁₉	—	4	3	no	—
174	C₂×C₄×C₁₉	—	4	6	no	—
175	C₂×C₄×C₁₉	—	4	3	no	—
176	C₂×C₄×C₁₉	—	4	3	no	—
177	C₂×C₄×C₁₉	—	4	3	no	—
178	C₂×C₄×C₁₉	—	4	3	no	—
179	C₂×C₄×C₁₉	—	4	3	no	—
180	C₂×C₄×C₁₉	—	4	3	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	4	3	no	—
183	C₂×C₄×C₁₉	—	4	3	no	—
184	C₂×C₄×C₁₉	—	4	3	no	—
185	C₂×C₄×C₁₉	—	4	3	no	—
186	C₂×C₄×C₁₉	—	8	3	no	—
187	C₂×C₄×C₁₉	—	8	3	no	—
188	C₂×C₄×C₁₉	—	8	3	no	—
189	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#120	1	3	yes	—
191	C₂×C₄×C₁₉	#121	1	6	yes	—
192	C₄×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂×#458	C₂×C₁₉	1	1	yes	characteristic, complemented
194	C₂×B(4,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
195	#2534	C₂×C₁₉	1	3	yes	complemented
196	#1890	C₂×C₁₉	1	3	yes	complemented
197	#1889	C₂×C₁₉	1	3	yes	complemented
198	#1799	C₂×C₁₉	1	3	yes	complemented
199	C₂²×C₁₉	—	2	3	no	—
200	C₂²×C₁₉	—	2	3	no	—
201	C₂²×C₁₉	—	2	6	no	—
202	C₂²×C₁₉	—	4	1	no	—
203	C₂²×C₁₉	—	4	3	no	—
204	C₂²×C₁₉	—	4	6	no	—
205	C₂²×C₁₉	—	4	6	no	—
206	C₂²×C₁₉	—	4	6	no	—
207	C₂²×C₁₉	—	4	3	no	—
208	C₂²×C₁₉	—	4	3	no	—
209	C₂²×C₁₉	—	4	2	no	—
210	C₂²×C₁₉	—	8	3	no	—
211	C₂²×C₁₉	—	8	3	no	—
212	C₂²×C₁₉	—	8	3	no	—
213	C₂²×C₁₉	—	8	4	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	8	1	no	—
216	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×#121	1	3	yes	—
218	C₂²×C₁₉	#525	1	3	yes	—
219	C₄×C₁₉	—	2	6	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	3	no	—
222	C₄×C₁₉	—	4	3	no	—
223	C₄×C₁₉	—	4	3	no	—
224	C₄×C₁₉	—	8	3	no	—
225	C₄×C₁₉	—	8	3	no	—
226	C₄×C₁₉	—	8	1	no	—
227	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	1	yes	characteristic
228	C₂×#123	C₂²×C₁₉	1	3	yes	—
229	C₂×#120	C₂²×C₁₉	1	3	yes	—
230	#520	—	2	3	no	—
231	#518	—	2	3	no	—
232	#518	C₂²×C₁₉	1	3	yes	—
233	C₄×#41	—	2	3	no	—
234	C₂×C₄×D₄	—	2	3	no	—
235	C₂×C₄×D₄	C₂²×C₁₉	1	3	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
237	#458	—	2	4	no	—
238	B(4,𝔽₂)	—	2	4	no	—
239	C₂×#99	C₂²×C₁₉	1	3	yes	—
240	C₂×#99	C₂²×C₁₉	1	3	yes	—
241	#396	—	2	3	no	—
242	#394	—	2	3	no	—
243	#388	—	2	3	no	—
244	#386	—	2	3	no	—
245	#381	C₂²×C₁₉	1	3	yes	complemented
246	#380	C₂²×C₁₉	1	3	yes	complemented
247	#379	C₂²×C₁₉	1	3	yes	complemented
248	#342	C₂²×C₁₉	1	6	yes	complemented
249	C₂×C₁₉	—	2	3	no	—
250	C₂×C₁₉	—	2	3	no	—
251	C₂×C₁₉	—	4	6	no	—
252	C₂×C₁₉	—	8	2	no	—
253	C₂×C₁₉	#2847	1	1	yes	characteristic
254	C₂×C₁₉	#3025	1	1	yes	characteristic
255	C₂×C₁₉	#3026	1	1	yes	characteristic
256	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
257	H(5,𝔽₂)	—	2	6	no	—
258	H(5,𝔽₂)	D₄×C₁₉	1	4	yes	—
259	C₂×#41	—	2	3	no	—
260	C₂²×D₄	—	2	3	no	—
261	C₂²×D₄	—	2	3	no	—
262	C₂²×D₄	C₂³×C₁₉	1	3	yes	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	D₄×C₁₉	1	3	yes	complemented
265	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
267	#123	—	2	6	no	—
268	#123	—	2	6	no	—
269	#120	—	2	6	no	—
270	#120	—	2	6	no	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×Q₈	—	2	3	no	—
273	C₄×D₄	—	2	3	no	—
274	C₄×D₄	—	2	6	no	—
275	C₄×D₄	—	2	3	no	—
276	C₄×D₄	—	2	6	no	—
277	C₄×D₄	—	2	6	no	—
278	C₄×D₄	—	2	6	no	—
279	C₄×D₄	—	2	6	no	—
280	#117	—	2	6	no	—
281	#117	—	2	3	no	—
282	C₂×C₄⋊C₄	—	2	3	no	—
283	C₂×C₄⋊C₄	—	2	3	no	—
284	C₂×C₄⋊C₄	—	2	3	no	—
285	C₂×C₄⋊C₄	D₄×C₁₉	1	3	yes	complemented
286	C₂×C₂²⋊C₄	—	2	3	no	—
287	C₂×C₂²⋊C₄	—	2	3	no	—
288	C₂×C₂²⋊C₄	—	2	3	no	—
289	C₂×C₂²⋊C₄	—	2	3	no	—
290	C₂×C₂²⋊C₄	—	2	3	no	—
291	C₂×C₂²⋊C₄	—	2	3	no	—
292	C₂×C₂²⋊C₄	—	2	3	no	—
293	C₂×C₂²⋊C₄	—	2	3	no	—
294	C₂×C₂²⋊C₄	D₄×C₁₉	1	3	yes	complemented
295	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₉	1	3	yes	—
298	C₂×C₄²	—	2	3	no	—
299	C₂×C₄²	D₄×C₁₉	1	3	yes	complemented
300	#99	—	2	6	no	—
301	#99	—	2	6	no	—
302	#95	—	2	3	no	—
303	#95	—	2	3	no	—
304	#95	—	2	3	no	—
305	C₁₉	#32928	1	1	yes	characteristic, direct product factor, Sylow
306	C₂⁴	—	2	1	no	—
307	C₂⁴	—	2	3	no	—
308	C₂⁴	—	2	1	no	—
309	C₂⁴	—	2	3	no	—
310	C₂⁴	—	4	2	no	—
311	C₂⁴	—	8	1	no	—
312	C₂⁴	C₂×D₄×C₁₉	1	3	yes	—
313	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
314	#41	—	2	12	no	—
315	#41	—	2	12	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×D₄	—	2	3	no	—
318	C₂×D₄	—	2	12	no	—
319	C₂×D₄	—	2	12	no	—
320	C₂×D₄	—	2	6	no	—
321	C₂×D₄	—	2	6	no	—
322	C₂×D₄	—	4	6	no	—
323	C₂×D₄	—	4	6	no	—
324	C₂×D₄	—	8	3	no	—
325	C₂×D₄	C₂×D₄×C₁₉	1	6	yes	—
326	C₂×D₄	#41×C₁₉	1	6	yes	—
327	C₂²×C₄	—	2	3	no	—
328	C₂²×C₄	—	2	3	no	—
329	C₂²×C₄	—	2	3	no	—
330	C₂²×C₄	—	2	3	no	—
331	C₂²×C₄	—	2	3	no	—
332	C₂²×C₄	—	2	3	no	—
333	C₂²×C₄	—	2	3	no	—
334	C₂²×C₄	—	2	3	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	3	no	—
337	C₂²×C₄	—	8	1	no	—
338	C₂²×C₄	—	8	3	no	—
339	C₂²×C₄	—	8	2	no	—
340	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
341	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
342	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
343	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
344	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
345	C₄⋊C₄	—	2	3	no	—
346	C₄⋊C₄	—	2	3	no	—
347	C₄⋊C₄	—	2	6	no	—
348	C₄⋊C₄	—	4	6	no	—
349	C₄⋊C₄	—	8	3	no	—
350	C₂²⋊C₄	—	2	6	no	—
351	C₂²⋊C₄	—	2	6	no	—
352	C₂²⋊C₄	—	2	6	no	—
353	C₂²⋊C₄	—	2	3	no	—
354	C₂²⋊C₄	—	2	3	no	—
355	C₂²⋊C₄	—	2	3	no	—
356	C₂²⋊C₄	—	2	3	no	—
357	C₂²⋊C₄	—	4	6	no	—
358	C₂²⋊C₄	—	4	6	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	3	no	—
361	C₂²⋊C₄	—	4	6	no	—
362	C₂²⋊C₄	—	8	3	no	—
363	C₄²	—	2	6	no	—
364	C₄²	—	2	3	no	—
365	C₄²	—	2	3	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	3	no	—
368	C₂³	—	2	3	no	—
369	C₂³	—	2	6	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	3	no	—
373	C₂³	—	4	3	no	—
374	C₂³	—	4	3	no	—
375	C₂³	—	4	3	no	—
376	C₂³	—	4	3	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	4	3	no	—
379	C₂³	—	4	3	no	—
380	C₂³	—	8	2	no	—
381	C₂³	—	8	6	no	—
382	C₂³	—	8	1	no	—
383	C₂³	—	8	1	no	—
384	C₂³	C₁₉×#121	1	6	yes	—
385	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
386	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
387	C₂³	C₂×#41×C₁₉	1	3	yes	—
388	Q₈	—	2	4	no	—
389	D₄	—	2	12	no	—
390	D₄	—	2	12	no	—
391	D₄	—	2	12	no	—
392	D₄	—	8	12	no	—
393	C₂×C₄	—	2	12	no	—
394	C₂×C₄	—	2	3	no	—
395	C₂×C₄	—	2	3	no	—
396	C₂×C₄	—	2	3	no	—
397	C₂×C₄	—	2	3	no	—
398	C₂×C₄	—	4	3	no	—
399	C₂×C₄	—	4	3	no	—
400	C₂×C₄	—	4	6	no	—
401	C₂×C₄	—	4	3	no	—
402	C₂×C₄	—	4	3	no	—
403	C₂×C₄	—	4	3	no	—
404	C₂×C₄	—	4	3	no	—
405	C₂×C₄	—	4	3	no	—
406	C₂×C₄	—	4	3	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	3	no	—
409	C₂×C₄	—	4	3	no	—
410	C₂×C₄	—	4	3	no	—
411	C₂×C₄	—	4	3	no	—
412	C₂×C₄	—	8	3	no	—
413	C₂×C₄	—	8	3	no	—
414	C₂×C₄	—	8	3	no	—
415	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
416	C₂×C₄	C₁₉×#120	1	3	yes	—
417	C₂×C₄	C₁₉×#121	1	6	yes	—
418	C₂²	—	2	3	no	—
419	C₂²	—	2	3	no	—
420	C₂²	—	2	6	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	3	no	—
423	C₂²	—	4	6	no	—
424	C₂²	—	4	6	no	—
425	C₂²	—	4	6	no	—
426	C₂²	—	4	3	no	—
427	C₂²	—	4	3	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	3	no	—
430	C₂²	—	8	3	no	—
431	C₂²	—	8	3	no	—
432	C₂²	—	8	4	no	—
433	C₂²	—	8	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
436	C₂²	C₂×C₁₉×#121	1	3	yes	—
437	C₂²	C₁₉×#525	1	3	yes	—
438	C₄	—	2	1	no	—
439	C₄	—	2	3	no	—
440	C₄	—	2	6	no	—
441	C₄	—	4	3	no	—
442	C₄	—	4	3	no	—
443	C₄	—	8	3	no	—
444	C₄	—	8	3	no	—
445	C₄	—	8	1	no	—
446	C₂	—	2	3	no	—
447	C₂	—	2	3	no	—
448	C₂	—	4	6	no	—
449	C₂	—	8	2	no	—
450	C₂	C₁₉×#2847	1	1	yes	characteristic
451	C₂	C₁₉×#3025	1	1	yes	characteristic
452	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂×C₁₉×B(4,𝔽₂)	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₁₉×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₁₉×#458	C₂	semidirect
4. C₁₉×#2534	C₂	semidirect
5. C₁₉×#1890	C₂	semidirect
6. C₁₉×#1889	C₂	semidirect
7. C₁₉×#1799	C₂	semidirect
17. C₂²×C₂²⋊C₄×C₁₉	C₂²	semidirect
26. C₁₉×#381	C₂²	semidirect
27. C₁₉×#380	C₂²	semidirect
28. C₁₉×#379	C₂²	semidirect
29. C₁₉×#342	C₂²	semidirect
38. C₂³×C₄×C₁₉	D₄	semidirect
59. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
68. C₂×C₂²⋊C₄×C₁₉	D₄	semidirect
73. C₂×C₄²×C₁₉	D₄	semidirect
139. #32928	C₁₉	direct (N × H)
192. C₄×H(5,𝔽₂)	C₂×C₁₉	semidirect
193. C₂×#458	C₂×C₁₉	semidirect
195. #2534	C₂×C₁₉	semidirect
196. #1890	C₂×C₁₉	semidirect
197. #1889	C₂×C₁₉	semidirect
198. #1799	C₂×C₁₉	semidirect
236. C₂²×C₂²⋊C₄	C₂²×C₁₉	semidirect
245. #381	C₂²×C₁₉	semidirect
246. #380	C₂²×C₁₉	semidirect
247. #379	C₂²×C₁₉	semidirect
248. #342	C₂²×C₁₉	semidirect
264. C₂³×C₄	D₄×C₁₉	semidirect
285. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
294. C₂×C₂²⋊C₄	D₄×C₁₉	semidirect
299. C₂×C₄²	D₄×C₁₉	semidirect
305. C₁₉	#32928	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₉×H(5,𝔽₂)	2
C₂×C₁₉×#458	2
C₂×C₁₉×B(4,𝔽₂)	2
C₁₉×#2534	2
C₁₉×#1890	2
C₁₉×#1889	2
C₁₉×#1799	2
#32928	19

Subgroups — C19×#32928 #18038887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32928 #18038887