Subgroups — C₁₉×#20616 #18026575

Order 4864.

3986 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#421	C₂	1	2	yes	maximal, complemented
3	C₁₉×#2896	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#1792	C₂	1	8	yes	maximal, complemented
7	C₂×C₁₉×H(5,𝔽₂)	—	2	8	no	—
8	C₂×C₁₉×H(5,𝔽₂)	—	2	4	no	—
9	C₂×C₁₉×H(5,𝔽₂)	—	2	4	no	—
10	C₂×C₁₉×H(5,𝔽₂)	—	2	2	no	—
11	C₂×C₁₉×H(5,𝔽₂)	C₄	1	8	yes	complemented
12	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	4	yes	—
13	C₂²×#41×C₁₉	—	2	2	no	—
14	C₂²×#41×C₁₉	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₉	—	2	2	no	—
16	C₂³×D₄×C₁₉	—	2	2	no	—
17	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic, complemented
21	C₁₉×#421	—	2	8	no	—
22	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
23	C₁₉×#419	—	2	2	no	—
24	C₁₉×#418	—	2	2	no	—
25	C₁₉×#417	C₂²	1	8	yes	complemented
26	C₁₉×#416	—	2	4	no	—
27	C₂×C₁₉×#100	—	2	4	no	—
28	C₂×C₁₉×#100	C₂²	1	4	yes	complemented
29	C₁₉×#390	—	2	2	no	—
30	C₁₉×#390	C₂²	1	4	yes	complemented
31	C₁₉×#379	—	2	2	no	—
32	C₂⁵×C₁₉	—	2	2	no	—
33	C₂⁵×C₁₉	D₄	1	2	yes	—
34	C₁₉×H(5,𝔽₂)	—	2	16	no	—
35	C₁₉×H(5,𝔽₂)	—	2	32	no	—
36	C₁₉×H(5,𝔽₂)	—	2	32	no	—
37	C₁₉×H(5,𝔽₂)	—	2	16	no	—
38	C₁₉×H(5,𝔽₂)	—	2	16	no	—
39	C₁₉×H(5,𝔽₂)	—	2	8	no	—
40	C₁₉×H(5,𝔽₂)	C₂×C₄	1	16	yes	—
41	C₂×#41×C₁₉	—	2	8	no	—
42	C₂×#41×C₁₉	—	2	16	no	—
43	C₂×#41×C₁₉	—	2	16	no	—
44	C₂×#41×C₁₉	—	2	8	no	—
45	C₂×#41×C₁₉	—	2	4	no	—
46	C₂×#41×C₁₉	—	2	2	no	—
47	C₂×#41×C₁₉	—	2	4	no	—
48	C₂×#41×C₁₉	—	2	2	no	—
49	C₂×#41×C₁₉	C₂×C₄	1	8	yes	—
50	C₂×#41×C₁₉	D₄	1	8	yes	—
51	C₂×#41×C₁₉	D₄	1	4	yes	—
52	C₂×#41×C₁₉	C₂³	1	4	yes	—
53	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
54	C₂²×D₄×C₁₉	—	2	4	no	—
55	C₂²×D₄×C₁₉	—	2	8	no	—
56	C₂²×D₄×C₁₉	—	2	16	no	—
57	C₂²×D₄×C₁₉	—	2	8	no	—
58	C₂²×D₄×C₁₉	—	2	16	no	—
59	C₂²×D₄×C₁₉	—	2	16	no	—
60	C₂²×D₄×C₁₉	—	2	2	no	—
61	C₂²×D₄×C₁₉	—	2	8	no	—
62	C₂²×D₄×C₁₉	—	2	16	no	—
63	C₂²×D₄×C₁₉	—	2	8	no	—
64	C₂²×D₄×C₁₉	—	2	2	no	—
65	C₂²×D₄×C₁₉	—	2	2	no	—
66	C₂²×D₄×C₁₉	—	2	4	no	—
67	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
68	C₂²×D₄×C₁₉	D₄	1	2	yes	—
69	C₂²×D₄×C₁₉	D₄	1	4	yes	—
70	C₂²×D₄×C₁₉	D₄	1	2	yes	—
71	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₉	—	2	2	no	—
73	C₂³×C₄×C₁₉	—	2	2	no	—
74	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₁₉	—	2	2	no	—
76	C₂×M₁₆×C₁₉	—	2	4	no	—
77	C₂×M₁₆×C₁₉	—	2	4	no	—
78	C₂×M₁₆×C₁₉	C₂³	1	4	yes	complemented
79	C₂²×C₈×C₁₉	—	2	2	no	—
80	C₁₉×#117	—	2	4	no	—
81	C₁₉×#117	—	2	2	no	—
82	C₁₉×#117	—	2	2	no	—
83	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	complemented
85	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
88	C₂×C₄²×C₁₉	—	2	1	no	—
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	complemented
90	C₁₉×#104	—	2	16	no	—
91	C₁₉×#103	—	2	8	no	—
92	C₁₉×#102	—	2	8	no	—
93	C₁₉×#100	—	2	8	no	—
94	C₂⁴×C₁₉	—	2	8	no	—
95	C₂⁴×C₁₉	—	2	16	no	—
96	C₂⁴×C₁₉	—	2	2	no	—
97	C₂⁴×C₁₉	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	4	no	—
100	C₂⁴×C₁₉	—	8	4	no	—
101	C₂⁴×C₁₉	—	8	8	no	—
102	C₂⁴×C₁₉	C₂²⋊C₄	1	8	yes	—
103	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
104	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
105	#41×C₁₉	—	2	32	no	—
106	#41×C₁₉	—	2	64	no	—
107	#41×C₁₉	—	2	32	no	—
108	#41×C₁₉	—	2	8	no	—
109	#41×C₁₉	—	2	8	no	—
110	#41×C₁₉	—	2	8	no	—
111	#41×C₁₉	—	2	8	no	—
112	#41×C₁₉	—	2	8	no	—
113	#41×C₁₉	—	2	4	no	—
114	#41×C₁₉	—	2	4	no	—
115	#41×C₁₉	C₂²⋊C₄	1	16	yes	complemented
116	#41×C₁₉	C₂²×C₄	1	8	yes	—
117	#41×C₁₉	C₂×D₄	1	8	yes	—
118	C₂×Q₈×C₁₉	—	2	2	no	—
119	C₂×Q₈×C₁₉	—	2	4	no	—
120	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	complemented
121	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
122	C₂×D₄×C₁₉	—	2	16	no	—
123	C₂×D₄×C₁₉	—	2	32	no	—
124	C₂×D₄×C₁₉	—	2	32	no	—
125	C₂×D₄×C₁₉	—	2	64	no	—
126	C₂×D₄×C₁₉	—	2	32	no	—
127	C₂×D₄×C₁₉	—	2	64	no	—
128	C₂×D₄×C₁₉	—	2	8	no	—
129	C₂×D₄×C₁₉	—	2	32	no	—
130	C₂×D₄×C₁₉	—	2	4	no	—
131	C₂×D₄×C₁₉	—	2	8	no	—
132	C₂×D₄×C₁₉	—	2	4	no	—
133	C₂×D₄×C₁₉	—	2	32	no	—
134	C₂×D₄×C₁₉	—	2	8	no	—
135	C₂×D₄×C₁₉	—	2	8	no	—
136	C₂×D₄×C₁₉	—	2	8	no	—
137	C₂×D₄×C₁₉	—	2	4	no	—
138	C₂×D₄×C₁₉	—	2	4	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	8	no	—
141	C₂×D₄×C₁₉	—	2	4	no	—
142	C₂×D₄×C₁₉	—	2	4	no	—
143	C₂×D₄×C₁₉	—	2	4	no	—
144	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	—
145	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	complemented
146	C₂×D₄×C₁₉	C₂²×C₄	1	4	yes	—
147	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
148	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₉	—	2	8	no	—
150	C₂²×C₄×C₁₉	—	2	16	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	8	no	—
153	C₂²×C₄×C₁₉	—	2	4	no	—
154	C₂²×C₄×C₁₉	—	2	8	no	—
155	C₂²×C₄×C₁₉	—	2	4	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
165	M₁₆×C₁₉	—	2	4	no	—
166	M₁₆×C₁₉	—	2	4	no	—
167	M₁₆×C₁₉	—	4	4	no	—
168	C₂×C₈×C₁₉	—	2	4	no	—
169	C₂×C₈×C₁₉	—	4	4	no	—
170	C₄⋊C₄×C₁₉	—	2	4	no	—
171	C₄⋊C₄×C₁₉	—	4	2	no	—
172	C₂²⋊C₄×C₁₉	—	4	2	no	—
173	C₂²⋊C₄×C₁₉	—	4	1	no	—
174	C₂²⋊C₄×C₁₉	—	4	1	no	—
175	C₂²⋊C₄×C₁₉	—	8	8	no	—
176	C₄²×C₁₉	—	2	4	no	—
177	C₄²×C₁₉	—	4	2	no	—
178	#20616	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂³×C₁₉	—	2	32	no	—
180	C₂³×C₁₉	—	2	4	no	—
181	C₂³×C₁₉	—	2	4	no	—
182	C₂³×C₁₉	—	2	8	no	—
183	C₂³×C₁₉	—	2	8	no	—
184	C₂³×C₁₉	—	2	4	no	—
185	C₂³×C₁₉	—	2	8	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	8	no	—
188	C₂³×C₁₉	—	4	8	no	—
189	C₂³×C₁₉	—	4	8	no	—
190	C₂³×C₁₉	—	8	4	no	—
191	C₂³×C₁₉	—	8	8	no	—
192	C₂³×C₁₉	—	8	8	no	—
193	C₂³×C₁₉	—	8	32	no	—
194	C₂³×C₁₉	—	8	16	no	—
195	C₂³×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
196	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂³×C₁₉	#120	1	1	yes	characteristic
198	C₂³×C₁₉	#120	1	1	yes	characteristic
199	C₂³×C₁₉	#120	1	2	yes	—
200	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₁₉	—	2	4	no	—
202	Q₈×C₁₉	—	2	8	no	—
203	Q₈×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
204	D₄×C₁₉	—	2	64	no	—
205	D₄×C₁₉	—	2	8	no	—
206	D₄×C₁₉	—	2	8	no	—
207	D₄×C₁₉	—	2	16	no	—
208	D₄×C₁₉	—	2	8	no	—
209	D₄×C₁₉	—	2	8	no	—
210	D₄×C₁₉	—	2	4	no	—
211	D₄×C₁₉	—	2	16	no	—
212	D₄×C₁₉	—	2	8	no	—
213	D₄×C₁₉	C₂×C₂²⋊C₄	1	8	yes	—
214	C₂×C₄×C₁₉	—	2	32	no	—
215	C₂×C₄×C₁₉	—	2	4	no	—
216	C₂×C₄×C₁₉	—	2	8	no	—
217	C₂×C₄×C₁₉	—	2	8	no	—
218	C₂×C₄×C₁₉	—	2	8	no	—
219	C₂×C₄×C₁₉	—	2	16	no	—
220	C₂×C₄×C₁₉	—	4	4	no	—
221	C₂×C₄×C₁₉	—	4	4	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
225	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
226	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂×C₄×C₁₉	#120	1	4	yes	—
228	C₂×C₄×C₁₉	#120	1	4	yes	—
229	C₂×C₄×C₁₉	#120	1	2	yes	—
230	C₂×C₄×C₁₉	#120	1	2	yes	—
231	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
235	C₈×C₁₉	—	4	4	no	—
236	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic
237	C₂×#421	C₂×C₁₉	1	2	yes	complemented
238	#2896	C₂×C₁₉	1	2	yes	complemented
239	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#2309	C₂×C₁₉	1	1	yes	characteristic, complemented
241	#1792	C₂×C₁₉	1	8	yes	complemented
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	2	2	no	—
244	C₂²×C₁₉	—	2	2	no	—
245	C₂²×C₁₉	—	2	8	no	—
246	C₂²×C₁₉	—	2	8	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	4	2	no	—
249	C₂²×C₁₉	—	4	8	no	—
250	C₂²×C₁₉	—	4	16	no	—
251	C₂²×C₁₉	—	4	16	no	—
252	C₂²×C₁₉	—	4	8	no	—
253	C₂²×C₁₉	—	4	8	no	—
254	C₂²×C₁₉	—	8	4	no	—
255	C₂²×C₁₉	—	8	8	no	—
256	C₂²×C₁₉	—	8	32	no	—
257	C₂²×C₁₉	#379	1	2	yes	—
258	C₂²×C₁₉	#379	1	2	yes	—
259	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
261	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
262	C₄×C₁₉	—	2	8	no	—
263	C₄×C₁₉	—	8	2	no	—
264	C₄×C₁₉	—	8	2	no	—
265	C₄×C₁₉	#379	1	4	yes	—
266	C₄×C₁₉	C₂²×C₂²⋊C₄	1	2	yes	—
267	C₄×C₁₉	C₂×#120	1	2	yes	—
268	C₂×H(5,𝔽₂)	—	2	8	no	—
269	C₂×H(5,𝔽₂)	—	2	4	no	—
270	C₂×H(5,𝔽₂)	—	2	4	no	—
271	C₂×H(5,𝔽₂)	—	2	2	no	—
272	C₂×H(5,𝔽₂)	C₄×C₁₉	1	8	yes	complemented
273	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	4	yes	—
274	C₂²×#41	—	2	2	no	—
275	C₂²×#41	C₂²×C₁₉	1	2	yes	—
276	C₂³×D₄	—	2	2	no	—
277	C₂³×D₄	—	2	2	no	—
278	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
279	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
280	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
281	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic, complemented
282	#421	—	2	8	no	—
283	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
284	#419	—	2	2	no	—
285	#418	—	2	2	no	—
286	#417	C₂²×C₁₉	1	8	yes	complemented
287	#416	—	2	4	no	—
288	C₂×#100	—	2	4	no	—
289	C₂×#100	C₂²×C₁₉	1	4	yes	complemented
290	#390	—	2	2	no	—
291	#390	C₂²×C₁₉	1	4	yes	complemented
292	#379	—	2	2	no	—
293	C₂×C₁₉	—	2	1	no	—
294	C₂×C₁₉	—	2	2	no	—
295	C₂×C₁₉	—	2	1	no	—
296	C₂×C₁₉	—	2	2	no	—
297	C₂×C₁₉	—	4	8	no	—
298	C₂×C₁₉	—	4	8	no	—
299	C₂×C₁₉	C₂×#379	1	1	yes	characteristic
300	C₂×C₁₉	#3019	1	2	yes	—
301	C₂⁵	—	2	2	no	—
302	C₂⁵	D₄×C₁₉	1	2	yes	—
303	H(5,𝔽₂)	—	2	32	no	—
304	H(5,𝔽₂)	—	2	16	no	—
305	H(5,𝔽₂)	—	2	32	no	—
306	H(5,𝔽₂)	—	2	16	no	—
307	H(5,𝔽₂)	—	2	16	no	—
308	H(5,𝔽₂)	—	2	8	no	—
309	H(5,𝔽₂)	C₂×C₄×C₁₉	1	16	yes	—
310	C₂×#41	—	2	16	no	—
311	C₂×#41	—	2	8	no	—
312	C₂×#41	—	2	16	no	—
313	C₂×#41	—	2	8	no	—
314	C₂×#41	—	2	4	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	2	4	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	C₂×C₄×C₁₉	1	8	yes	—
319	C₂×#41	D₄×C₁₉	1	8	yes	—
320	C₂×#41	D₄×C₁₉	1	4	yes	—
321	C₂×#41	C₂³×C₁₉	1	4	yes	—
322	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
323	C₂²×D₄	—	2	4	no	—
324	C₂²×D₄	—	2	16	no	—
325	C₂²×D₄	—	2	8	no	—
326	C₂²×D₄	—	2	16	no	—
327	C₂²×D₄	—	2	8	no	—
328	C₂²×D₄	—	2	16	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	8	no	—
331	C₂²×D₄	—	2	16	no	—
332	C₂²×D₄	—	2	8	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	—	2	4	no	—
336	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
337	C₂²×D₄	D₄×C₁₉	1	2	yes	—
338	C₂²×D₄	D₄×C₁₉	1	4	yes	—
339	C₂²×D₄	D₄×C₁₉	1	2	yes	—
340	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
341	C₂³×C₄	—	2	2	no	—
342	C₂³×C₄	—	2	2	no	—
343	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
344	C₂×M₁₆	—	2	2	no	—
345	C₂×M₁₆	—	2	4	no	—
346	C₂×M₁₆	—	2	4	no	—
347	C₂×M₁₆	C₂³×C₁₉	1	4	yes	complemented
348	C₂²×C₈	—	2	2	no	—
349	#117	—	2	4	no	—
350	#117	—	2	2	no	—
351	#117	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	complemented
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	8	no	—
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₂³×C₁₉	1	2	yes	complemented
359	#104	—	2	16	no	—
360	#103	—	2	8	no	—
361	#102	—	2	8	no	—
362	#100	—	2	8	no	—
363	C₁₉	#20616	1	1	yes	characteristic, direct product factor, Sylow
364	C₂⁴	—	2	16	no	—
365	C₂⁴	—	2	8	no	—
366	C₂⁴	—	2	2	no	—
367	C₂⁴	—	2	2	no	—
368	C₂⁴	—	2	4	no	—
369	C₂⁴	—	2	2	no	—
370	C₂⁴	—	8	4	no	—
371	C₂⁴	—	8	8	no	—
372	C₂⁴	C₂²⋊C₄×C₁₉	1	8	yes	—
373	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
374	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
375	#41	—	2	64	no	—
376	#41	—	2	32	no	—
377	#41	—	2	32	no	—
378	#41	—	2	8	no	—
379	#41	—	2	8	no	—
380	#41	—	2	8	no	—
381	#41	—	2	8	no	—
382	#41	—	2	8	no	—
383	#41	—	2	4	no	—
384	#41	—	2	4	no	—
385	#41	C₂²⋊C₄×C₁₉	1	16	yes	complemented
386	#41	C₂²×C₄×C₁₉	1	8	yes	—
387	#41	C₂×D₄×C₁₉	1	8	yes	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	C₂²⋊C₄×C₁₉	1	8	yes	complemented
391	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
392	C₂×D₄	—	2	32	no	—
393	C₂×D₄	—	2	16	no	—
394	C₂×D₄	—	2	64	no	—
395	C₂×D₄	—	2	32	no	—
396	C₂×D₄	—	2	64	no	—
397	C₂×D₄	—	2	32	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂×D₄	—	2	32	no	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	32	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	8	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
415	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	complemented
416	C₂×D₄	C₂²×C₄×C₁₉	1	4	yes	—
417	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
418	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
419	C₂²×C₄	—	2	16	no	—
420	C₂²×C₄	—	2	8	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	2	8	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
433	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
435	M₁₆	—	2	4	no	—
436	M₁₆	—	2	4	no	—
437	M₁₆	—	4	4	no	—
438	C₂×C₈	—	2	4	no	—
439	C₂×C₈	—	4	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	4	2	no	—
442	C₂²⋊C₄	—	4	2	no	—
443	C₂²⋊C₄	—	4	1	no	—
444	C₂²⋊C₄	—	4	1	no	—
445	C₂²⋊C₄	—	8	8	no	—
446	C₄²	—	2	4	no	—
447	C₄²	—	4	2	no	—
448	C₂³	—	2	32	no	—
449	C₂³	—	2	8	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	8	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	8	no	—
457	C₂³	—	4	8	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	8	4	no	—
460	C₂³	—	8	8	no	—
461	C₂³	—	8	8	no	—
462	C₂³	—	8	32	no	—
463	C₂³	—	8	16	no	—
464	C₂³	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
465	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
466	C₂³	C₁₉×#120	1	1	yes	characteristic
467	C₂³	C₁₉×#120	1	1	yes	characteristic
468	C₂³	C₁₉×#120	1	2	yes	—
469	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
470	Q₈	—	2	8	no	—
471	Q₈	—	2	4	no	—
472	Q₈	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
473	D₄	—	2	64	no	—
474	D₄	—	2	16	no	—
475	D₄	—	2	8	no	—
476	D₄	—	2	8	no	—
477	D₄	—	2	16	no	—
478	D₄	—	2	8	no	—
479	D₄	—	2	8	no	—
480	D₄	—	2	8	no	—
481	D₄	—	2	4	no	—
482	D₄	C₂×C₂²⋊C₄×C₁₉	1	8	yes	—
483	C₂×C₄	—	2	32	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	16	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
494	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
495	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
496	C₂×C₄	C₁₉×#120	1	2	yes	—
497	C₂×C₄	C₁₉×#120	1	2	yes	—
498	C₂×C₄	C₁₉×#120	1	4	yes	—
499	C₂×C₄	C₁₉×#120	1	4	yes	—
500	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
503	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	C₈	—	4	4	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	8	no	—
509	C₂²	—	2	8	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	8	no	—
513	C₂²	—	4	16	no	—
514	C₂²	—	4	16	no	—
515	C₂²	—	4	8	no	—
516	C₂²	—	4	8	no	—
517	C₂²	—	8	4	no	—
518	C₂²	—	8	8	no	—
519	C₂²	—	8	32	no	—
520	C₂²	C₁₉×#379	1	2	yes	—
521	C₂²	C₁₉×#379	1	2	yes	—
522	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
523	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
524	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
525	C₄	—	2	8	no	—
526	C₄	—	8	2	no	—
527	C₄	—	8	2	no	—
528	C₄	C₁₉×#379	1	4	yes	—
529	C₄	C₂²×C₂²⋊C₄×C₁₉	1	2	yes	—
530	C₄	C₂×C₁₉×#120	1	2	yes	—
531	C₂	—	2	1	no	—
532	C₂	—	2	2	no	—
533	C₂	—	2	1	no	—
534	C₂	—	2	2	no	—
535	C₂	—	4	8	no	—
536	C₂	—	4	8	no	—
537	C₂	C₂×C₁₉×#379	1	1	yes	characteristic
538	C₂	C₁₉×#3019	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×C₁₉×H(5,𝔽₂)	C₂
LCS	G ▷ C₂×C₄ ▷ 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
2. C₂×C₁₉×#421	C₂	semidirect
3. C₁₉×#2896	C₂	semidirect
4. C₂²×C₁₉×#100	C₂	semidirect
5. C₁₉×#2309	C₂	semidirect
6. C₁₉×#1792	C₂	semidirect
11. C₂×C₁₉×H(5,𝔽₂)	C₄	semidirect
18. C₂²×M₁₆×C₁₉	C₂²	semidirect
19. C₂×C₁₉×#117	C₂²	semidirect
20. C₂×C₁₉×#117	C₂²	semidirect
22. C₂×C₁₉×#104	C₂²	semidirect
25. C₁₉×#417	C₂²	semidirect
28. C₂×C₁₉×#100	C₂²	semidirect
30. C₁₉×#390	C₂²	semidirect
78. C₂×M₁₆×C₁₉	C₂³	semidirect
84. C₂×C₄⋊C₄×C₁₉	C₂³	semidirect
89. C₂×C₄²×C₁₉	C₂³	semidirect
115. #41×C₁₉	C₂²⋊C₄	semidirect
120. C₂×Q₈×C₁₉	C₂²⋊C₄	semidirect
145. C₂×D₄×C₁₉	C₂²⋊C₄	semidirect
178. #20616	C₁₉	direct (N × H)
237. C₂×#421	C₂×C₁₉	semidirect
238. #2896	C₂×C₁₉	semidirect
239. C₂²×#100	C₂×C₁₉	semidirect
240. #2309	C₂×C₁₉	semidirect
241. #1792	C₂×C₁₉	semidirect
272. C₂×H(5,𝔽₂)	C₄×C₁₉	semidirect
279. C₂²×M₁₆	C₂²×C₁₉	semidirect
280. C₂×#117	C₂²×C₁₉	semidirect
281. C₂×#117	C₂²×C₁₉	semidirect
283. C₂×#104	C₂²×C₁₉	semidirect
286. #417	C₂²×C₁₉	semidirect
289. C₂×#100	C₂²×C₁₉	semidirect
291. #390	C₂²×C₁₉	semidirect
347. C₂×M₁₆	C₂³×C₁₉	semidirect
353. C₂×C₄⋊C₄	C₂³×C₁₉	semidirect
358. C₂×C₄²	C₂³×C₁₉	semidirect
363. C₁₉	#20616	direct (N × H)
385. #41	C₂²⋊C₄×C₁₉	semidirect
390. C₂×Q₈	C₂²⋊C₄×C₁₉	semidirect
415. C₂×D₄	C₂²⋊C₄×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×H(5,𝔽₂)	2
C₂×C₁₉×#421	2
C₁₉×#2896	2
C₂²×C₁₉×#100	2
C₁₉×#2309	2
C₁₉×#1792	2
#20616	19

Subgroups — C19×#20616 #18026575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20616 #18026575