Subgroups — C₁₉×#25565 #18031524

Order 4864.

1312 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3490	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2483	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2412	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2062	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2044	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2030	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2022	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1898	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1890	C₂	1	2	yes	maximal, complemented
10	C₁₉×#1867	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₉×#342	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#551	—	2	2	no	—
13	C₁₉×#551	—	2	2	no	—
14	C₁₉×#546	—	2	2	no	—
15	C₁₉×#546	—	2	2	no	—
16	C₁₉×#543	C₂²	1	1	yes	characteristic
17	C₁₉×#538	—	2	1	no	—
18	C₁₉×#538	—	2	1	no	—
19	C₁₉×#534	C₂²	1	1	yes	characteristic
20	C₁₉×#525	—	2	1	no	—
21	C₁₉×#525	—	2	1	no	—
22	C₂×C₁₉×#123	C₂²	1	2	yes	—
23	C₂×C₁₉×#120	C₂²	1	2	yes	—
24	C₁₉×#518	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₂×C₁₉×#99	C₂²	1	2	yes	—
29	C₂×C₁₉×#99	C₂²	1	2	yes	—
30	C₁₉×#397	—	2	2	no	—
31	C₁₉×#397	—	2	1	no	—
32	C₁₉×#397	—	2	1	no	—
33	C₁₉×#394	—	2	2	no	—
34	C₁₉×#386	—	2	2	no	—
35	C₁₉×#386	C₂²	1	2	yes	—
36	C₁₉×#385	—	2	1	no	—
37	C₁₉×#385	C₂²	1	2	yes	—
38	C₁₉×#385	C₂²	1	1	yes	characteristic
39	C₁₉×#385	C₂²	1	1	yes	characteristic
40	C₁₉×#381	—	2	1	no	—
41	C₁₉×#381	C₂²	1	1	yes	characteristic
42	C₁₉×#381	C₂²	1	2	yes	—
43	C₁₉×#381	C₂²	1	1	yes	characteristic
44	C₁₉×#380	—	2	2	no	—
45	C₁₉×#379	C₂²	1	1	yes	characteristic
46	C₁₉×#342	C₂²	1	2	yes	—
47	C₁₉×#342	C₂²	1	2	yes	—
48	C₁₉×#342	C₂²	1	2	yes	—
49	C₁₉×#342	C₂²	1	1	yes	characteristic
50	C₁₉×#342	C₂²	1	1	yes	characteristic
51	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×#41×C₁₉	—	2	1	no	—
53	C₂×#41×C₁₉	—	2	1	no	—
54	C₂²×D₄×C₁₉	D₄	1	2	yes	—
55	C₂²×D₄×C₁₉	D₄	1	2	yes	—
56	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₉	—	2	2	no	—
58	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₁₉×#126	—	2	2	no	—
63	C₁₉×#126	—	2	2	no	—
64	C₁₉×#124	—	2	2	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#123	—	2	2	no	—
67	C₁₉×#123	—	2	2	no	—
68	C₁₉×#123	—	2	2	no	—
69	C₁₉×#123	—	2	2	no	—
70	C₁₉×#123	—	2	2	no	—
71	C₁₉×#123	—	2	4	no	—
72	C₁₉×#123	—	4	2	no	—
73	C₁₉×C₂²⋊Q₈	—	2	1	no	—
74	C₁₉×C₂²⋊Q₈	—	2	1	no	—
75	C₁₉×C₂²⋊Q₈	—	2	1	no	—
76	C₁₉×C₂²⋊Q₈	—	2	1	no	—
77	C₁₉×C₂²⋊Q₈	—	2	2	no	—
78	C₁₉×C₂²⋊Q₈	—	2	2	no	—
79	C₁₉×#121	—	2	1	no	—
80	C₁₉×#121	—	2	1	no	—
81	C₁₉×#121	—	2	2	no	—
82	C₁₉×#121	—	2	2	no	—
83	C₁₉×#121	—	2	1	no	—
84	C₁₉×#121	—	2	1	no	—
85	C₁₉×#120	—	2	2	no	—
86	C₁₉×#120	—	2	2	no	—
87	C₁₉×#120	—	2	2	no	—
88	C₁₉×#120	—	2	2	no	—
89	C₁₉×#120	—	2	2	no	—
90	C₄×D₄×C₁₉	—	2	2	no	—
91	C₄×D₄×C₁₉	—	2	2	no	—
92	C₄×D₄×C₁₉	—	2	2	no	—
93	C₄×D₄×C₁₉	—	2	2	no	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₁₉×#117	—	2	1	no	—
97	C₁₉×#117	—	2	1	no	—
98	C₁₉×#117	—	2	2	no	—
99	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
100	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
109	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
112	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
113	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
117	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
118	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
128	C₁₉×#99	—	2	4	no	—
129	C₁₉×#99	—	4	2	no	—
130	C₁₉×#95	—	2	2	no	—
131	C₁₉×#95	—	2	2	no	—
132	C₁₉×#95	—	2	1	no	—
133	C₁₉×#95	—	2	1	no	—
134	C₁₉×#95	—	2	1	no	—
135	C₁₉×#95	—	2	1	no	—
136	C₁₉×#95	—	2	1	no	—
137	C₁₉×#95	—	2	1	no	—
138	C₁₉×#95	—	2	2	no	—
139	C₁₉×#95	—	2	2	no	—
140	C₂⁴×C₁₉	—	2	2	no	—
141	C₂⁴×C₁₉	—	2	1	no	—
142	C₂⁴×C₁₉	—	2	1	no	—
143	C₂⁴×C₁₉	—	4	2	no	—
144	C₂⁴×C₁₉	—	8	1	no	—
145	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
146	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
148	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
149	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
151	#41×C₁₉	—	8	2	no	—
152	#41×C₁₉	—	8	2	no	—
153	C₂×Q₈×C₁₉	—	2	1	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×D₄×C₁₉	—	2	2	no	—
156	C₂×D₄×C₁₉	—	2	2	no	—
157	C₂×D₄×C₁₉	—	2	2	no	—
158	C₂×D₄×C₁₉	—	2	2	no	—
159	C₂×D₄×C₁₉	—	2	2	no	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	2	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	1	no	—
164	C₂×D₄×C₁₉	—	2	1	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	2	no	—
167	C₂×D₄×C₁₉	—	4	4	no	—
168	C₂×D₄×C₁₉	—	8	2	no	—
169	C₂²×C₄×C₁₉	—	2	1	no	—
170	C₂²×C₄×C₁₉	—	2	1	no	—
171	C₂²×C₄×C₁₉	—	2	2	no	—
172	C₂²×C₄×C₁₉	—	2	2	no	—
173	C₂²×C₄×C₁₉	—	2	2	no	—
174	C₂²×C₄×C₁₉	—	2	1	no	—
175	C₂²×C₄×C₁₉	—	2	1	no	—
176	C₂²×C₄×C₁₉	—	2	2	no	—
177	C₂²×C₄×C₁₉	—	2	2	no	—
178	C₂²×C₄×C₁₉	—	2	1	no	—
179	C₂²×C₄×C₁₉	—	2	1	no	—
180	C₂²×C₄×C₁₉	—	2	2	no	—
181	C₂²×C₄×C₁₉	—	2	1	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	2	no	—
184	C₂²×C₄×C₁₉	—	2	1	no	—
185	C₂²×C₄×C₁₉	—	2	1	no	—
186	C₂²×C₄×C₁₉	—	4	4	no	—
187	C₂²×C₄×C₁₉	—	4	2	no	—
188	C₂²×C₄×C₁₉	—	4	4	no	—
189	C₂²×C₄×C₁₉	—	8	1	no	—
190	C₂²×C₄×C₁₉	—	8	1	no	—
191	C₂²×C₄×C₁₉	—	8	2	no	—
192	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
193	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
195	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
199	C₄⋊C₄×C₁₉	—	2	2	no	—
200	C₄⋊C₄×C₁₉	—	2	2	no	—
201	C₄⋊C₄×C₁₉	—	2	1	no	—
202	C₄⋊C₄×C₁₉	—	2	1	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	2	no	—
206	C₄⋊C₄×C₁₉	—	2	2	no	—
207	C₄⋊C₄×C₁₉	—	4	4	no	—
208	C₄⋊C₄×C₁₉	—	8	2	no	—
209	C₄⋊C₄×C₁₉	—	8	1	no	—
210	C₄⋊C₄×C₁₉	—	8	1	no	—
211	C₂²⋊C₄×C₁₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	2	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	2	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	2	no	—
223	C₂²⋊C₄×C₁₉	—	2	2	no	—
224	C₂²⋊C₄×C₁₉	—	2	2	no	—
225	C₂²⋊C₄×C₁₉	—	2	2	no	—
226	C₂²⋊C₄×C₁₉	—	2	2	no	—
227	C₂²⋊C₄×C₁₉	—	2	2	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₉	—	2	1	no	—
230	C₂²⋊C₄×C₁₉	—	2	1	no	—
231	C₂²⋊C₄×C₁₉	—	4	4	no	—
232	C₂²⋊C₄×C₁₉	—	4	4	no	—
233	C₂²⋊C₄×C₁₉	—	4	2	no	—
234	C₂²⋊C₄×C₁₉	—	4	2	no	—
235	C₂²⋊C₄×C₁₉	—	4	1	no	—
236	C₂²⋊C₄×C₁₉	—	4	1	no	—
237	C₂²⋊C₄×C₁₉	—	8	1	no	—
238	C₂²⋊C₄×C₁₉	—	8	2	no	—
239	C₂²⋊C₄×C₁₉	#41	1	4	yes	complemented
240	C₄²×C₁₉	—	2	2	no	—
241	C₄²×C₁₉	—	2	2	no	—
242	#25565	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₁₉	—	2	1	no	—
244	C₂³×C₁₉	—	2	1	no	—
245	C₂³×C₁₉	—	2	2	no	—
246	C₂³×C₁₉	—	2	2	no	—
247	C₂³×C₁₉	—	2	2	no	—
248	C₂³×C₁₉	—	2	4	no	—
249	C₂³×C₁₉	—	2	1	no	—
250	C₂³×C₁₉	—	2	1	no	—
251	C₂³×C₁₉	—	2	2	no	—
252	C₂³×C₁₉	—	2	2	no	—
253	C₂³×C₁₉	—	2	2	no	—
254	C₂³×C₁₉	—	2	2	no	—
255	C₂³×C₁₉	—	2	2	no	—
256	C₂³×C₁₉	—	4	1	no	—
257	C₂³×C₁₉	—	4	2	no	—
258	C₂³×C₁₉	—	4	1	no	—
259	C₂³×C₁₉	—	4	1	no	—
260	C₂³×C₁₉	—	4	1	no	—
261	C₂³×C₁₉	—	4	2	no	—
262	C₂³×C₁₉	—	4	1	no	—
263	C₂³×C₁₉	—	4	2	no	—
264	C₂³×C₁₉	—	4	2	no	—
265	C₂³×C₁₉	—	4	2	no	—
266	C₂³×C₁₉	—	8	4	no	—
267	C₂³×C₁₉	—	8	2	no	—
268	C₂³×C₁₉	—	8	2	no	—
269	C₂³×C₁₉	#120	1	2	yes	—
270	C₂³×C₁₉	#120	1	1	yes	characteristic
271	C₂³×C₁₉	#120	1	1	yes	characteristic
272	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
273	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
274	C₂³×C₁₉	C₂×#41	1	2	yes	—
275	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
276	C₂³×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
277	Q₈×C₁₉	—	8	1	no	—
278	Q₈×C₁₉	—	8	1	no	—
279	D₄×C₁₉	—	4	4	no	—
280	D₄×C₁₉	—	4	2	no	—
281	D₄×C₁₉	—	4	2	no	—
282	D₄×C₁₉	—	4	2	no	—
283	D₄×C₁₉	—	4	2	no	—
284	D₄×C₁₉	—	4	4	no	—
285	D₄×C₁₉	—	8	2	no	—
286	D₄×C₁₉	—	8	2	no	—
287	D₄×C₁₉	—	8	1	no	—
288	D₄×C₁₉	—	8	1	no	—
289	C₂×C₄×C₁₉	—	2	2	no	—
290	C₂×C₄×C₁₉	—	2	1	no	—
291	C₂×C₄×C₁₉	—	2	1	no	—
292	C₂×C₄×C₁₉	—	2	2	no	—
293	C₂×C₄×C₁₉	—	2	2	no	—
294	C₂×C₄×C₁₉	—	2	1	no	—
295	C₂×C₄×C₁₉	—	2	1	no	—
296	C₂×C₄×C₁₉	—	2	4	no	—
297	C₂×C₄×C₁₉	—	2	2	no	—
298	C₂×C₄×C₁₉	—	2	2	no	—
299	C₂×C₄×C₁₉	—	4	2	no	—
300	C₂×C₄×C₁₉	—	4	2	no	—
301	C₂×C₄×C₁₉	—	4	2	no	—
302	C₂×C₄×C₁₉	—	4	2	no	—
303	C₂×C₄×C₁₉	—	4	1	no	—
304	C₂×C₄×C₁₉	—	4	1	no	—
305	C₂×C₄×C₁₉	—	4	2	no	—
306	C₂×C₄×C₁₉	—	4	1	no	—
307	C₂×C₄×C₁₉	—	4	1	no	—
308	C₂×C₄×C₁₉	—	4	2	no	—
309	C₂×C₄×C₁₉	—	4	1	no	—
310	C₂×C₄×C₁₉	—	4	1	no	—
311	C₂×C₄×C₁₉	—	4	1	no	—
312	C₂×C₄×C₁₉	—	4	1	no	—
313	C₂×C₄×C₁₉	—	4	2	no	—
314	C₂×C₄×C₁₉	—	4	2	no	—
315	C₂×C₄×C₁₉	—	4	1	no	—
316	C₂×C₄×C₁₉	—	4	1	no	—
317	C₂×C₄×C₁₉	—	4	2	no	—
318	C₂×C₄×C₁₉	—	4	2	no	—
319	C₂×C₄×C₁₉	—	4	1	no	—
320	C₂×C₄×C₁₉	—	4	1	no	—
321	C₂×C₄×C₁₉	—	4	1	no	—
322	C₂×C₄×C₁₉	—	4	1	no	—
323	C₂×C₄×C₁₉	—	4	1	no	—
324	C₂×C₄×C₁₉	—	4	1	no	—
325	C₂×C₄×C₁₉	—	4	2	no	—
326	C₂×C₄×C₁₉	—	4	2	no	—
327	C₂×C₄×C₁₉	—	4	2	no	—
328	C₂×C₄×C₁₉	—	8	1	no	—
329	C₂×C₄×C₁₉	—	8	1	no	—
330	C₂×C₄×C₁₉	—	8	2	no	—
331	C₂×C₄×C₁₉	—	8	2	no	—
332	C₂×C₄×C₁₉	—	8	8	no	—
333	#3490	C₂×C₁₉	1	1	yes	characteristic
334	#2483	C₂×C₁₉	1	1	yes	characteristic, complemented
335	#2412	C₂×C₁₉	1	2	yes	complemented
336	#2062	C₂×C₁₉	1	1	yes	characteristic, complemented
337	#2044	C₂×C₁₉	1	1	yes	characteristic, complemented
338	#2030	C₂×C₁₉	1	1	yes	characteristic, complemented
339	#2022	C₂×C₁₉	1	1	yes	characteristic, complemented
340	#1898	C₂×C₁₉	1	2	yes	complemented
341	#1890	C₂×C₁₉	1	2	yes	complemented
342	#1867	C₂×C₁₉	1	2	yes	complemented
343	C₂×#342	C₂×C₁₉	1	1	yes	characteristic, complemented
344	C₂²×C₁₉	—	2	1	no	—
345	C₂²×C₁₉	—	2	1	no	—
346	C₂²×C₁₉	—	2	2	no	—
347	C₂²×C₁₉	—	2	1	no	—
348	C₂²×C₁₉	—	2	2	no	—
349	C₂²×C₁₉	—	2	1	no	—
350	C₂²×C₁₉	—	2	1	no	—
351	C₂²×C₁₉	—	2	2	no	—
352	C₂²×C₁₉	—	2	1	no	—
353	C₂²×C₁₉	—	2	2	no	—
354	C₂²×C₁₉	—	2	1	no	—
355	C₂²×C₁₉	—	2	2	no	—
356	C₂²×C₁₉	—	4	2	no	—
357	C₂²×C₁₉	—	4	1	no	—
358	C₂²×C₁₉	—	4	1	no	—
359	C₂²×C₁₉	—	4	4	no	—
360	C₂²×C₁₉	—	4	2	no	—
361	C₂²×C₁₉	—	4	2	no	—
362	C₂²×C₁₉	—	4	4	no	—
363	C₂²×C₁₉	—	4	2	no	—
364	C₂²×C₁₉	—	4	2	no	—
365	C₂²×C₁₉	—	4	2	no	—
366	C₂²×C₁₉	—	8	2	no	—
367	C₂²×C₁₉	—	8	1	no	—
368	C₂²×C₁₉	—	8	1	no	—
369	C₂²×C₁₉	—	8	2	no	—
370	C₂²×C₁₉	—	8	2	no	—
371	C₂²×C₁₉	—	8	2	no	—
372	C₂²×C₁₉	#458	1	2	yes	—
373	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
374	C₂²×C₁₉	#532	1	1	yes	characteristic
375	C₂²×C₁₉	#537	1	1	yes	characteristic
376	C₂²×C₁₉	#546	1	2	yes	—
377	C₂²×C₁₉	#547	1	2	yes	—
378	C₄×C₁₉	—	4	4	no	—
379	C₄×C₁₉	—	4	2	no	—
380	C₄×C₁₉	—	4	1	no	—
381	C₄×C₁₉	—	4	1	no	—
382	C₄×C₁₉	—	4	2	no	—
383	C₄×C₁₉	—	4	1	no	—
384	C₄×C₁₉	—	4	1	no	—
385	C₄×C₁₉	—	4	2	no	—
386	C₄×C₁₉	—	8	1	no	—
387	C₄×C₁₉	—	8	1	no	—
388	C₄×C₁₉	—	8	2	no	—
389	C₄×C₁₉	—	8	1	no	—
390	C₄×C₁₉	—	8	1	no	—
391	#551	—	2	2	no	—
392	#551	—	2	2	no	—
393	#546	—	2	2	no	—
394	#546	—	2	2	no	—
395	#543	C₂²×C₁₉	1	1	yes	characteristic
396	#538	—	2	1	no	—
397	#538	—	2	1	no	—
398	#534	C₂²×C₁₉	1	1	yes	characteristic
399	#525	—	2	1	no	—
400	#525	—	2	1	no	—
401	C₂×#123	C₂²×C₁₉	1	2	yes	—
402	C₂×#120	C₂²×C₁₉	1	2	yes	—
403	#518	C₂²×C₁₉	1	2	yes	—
404	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
405	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
406	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
407	C₂×#99	C₂²×C₁₉	1	2	yes	—
408	C₂×#99	C₂²×C₁₉	1	2	yes	—
409	#397	—	2	2	no	—
410	#397	—	2	1	no	—
411	#397	—	2	1	no	—
412	#394	—	2	2	no	—
413	#386	—	2	2	no	—
414	#386	C₂²×C₁₉	1	2	yes	—
415	#385	—	2	1	no	—
416	#385	C₂²×C₁₉	1	2	yes	—
417	#385	C₂²×C₁₉	1	1	yes	characteristic
418	#385	C₂²×C₁₉	1	1	yes	characteristic
419	#381	—	2	1	no	—
420	#381	C₂²×C₁₉	1	1	yes	characteristic
421	#381	C₂²×C₁₉	1	2	yes	—
422	#381	C₂²×C₁₉	1	1	yes	characteristic
423	#380	—	2	2	no	—
424	#379	C₂²×C₁₉	1	1	yes	characteristic
425	#342	C₂²×C₁₉	1	2	yes	—
426	#342	C₂²×C₁₉	1	1	yes	characteristic
427	#342	C₂²×C₁₉	1	2	yes	—
428	#342	C₂²×C₁₉	1	2	yes	—
429	#342	C₂²×C₁₉	1	1	yes	characteristic
430	C₂×C₁₉	—	2	2	no	—
431	C₂×C₁₉	—	2	1	no	—
432	C₂×C₁₉	—	2	1	no	—
433	C₂×C₁₉	—	2	2	no	—
434	C₂×C₁₉	—	2	2	no	—
435	C₂×C₁₉	—	4	1	no	—
436	C₂×C₁₉	—	4	2	no	—
437	C₂×C₁₉	—	8	2	no	—
438	C₂×C₁₉	#2430	1	1	yes	characteristic
439	C₂×C₁₉	C₂×#458	1	1	yes	characteristic
440	C₂×C₁₉	#3026	1	1	yes	characteristic
441	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
442	C₂×#41	—	2	1	no	—
443	C₂×#41	—	2	1	no	—
444	C₂²×D₄	D₄×C₁₉	1	2	yes	—
445	C₂²×D₄	D₄×C₁₉	1	2	yes	—
446	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
447	C₂³×C₄	—	2	2	no	—
448	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
449	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
450	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
452	#126	—	2	2	no	—
453	#126	—	2	2	no	—
454	#124	—	2	2	no	—
455	#124	—	2	2	no	—
456	#123	—	2	2	no	—
457	#123	—	2	2	no	—
458	#123	—	2	2	no	—
459	#123	—	2	2	no	—
460	#123	—	2	2	no	—
461	#123	—	2	4	no	—
462	#123	—	4	2	no	—
463	C₂²⋊Q₈	—	2	1	no	—
464	C₂²⋊Q₈	—	2	1	no	—
465	C₂²⋊Q₈	—	2	1	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	#121	—	2	1	no	—
470	#121	—	2	1	no	—
471	#121	—	2	2	no	—
472	#121	—	2	2	no	—
473	#121	—	2	1	no	—
474	#121	—	2	1	no	—
475	#120	—	2	2	no	—
476	#120	—	2	2	no	—
477	#120	—	2	2	no	—
478	#120	—	2	2	no	—
479	#120	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	#117	—	2	1	no	—
487	#117	—	2	1	no	—
488	#117	—	2	2	no	—
489	C₂×C₄⋊C₄	—	2	2	no	—
490	C₂×C₄⋊C₄	—	2	2	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	2	no	—
494	C₂×C₂²⋊C₄	—	2	2	no	—
495	C₂×C₂²⋊C₄	—	2	2	no	—
496	C₂×C₂²⋊C₄	—	2	4	no	—
497	C₂×C₂²⋊C₄	—	2	2	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	2	no	—
500	C₂×C₂²⋊C₄	—	2	2	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	2	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	2	no	—
506	C₂×C₂²⋊C₄	—	4	2	no	—
507	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
508	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
510	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
518	#99	—	2	4	no	—
519	#99	—	4	2	no	—
520	#95	—	2	2	no	—
521	#95	—	2	2	no	—
522	#95	—	2	1	no	—
523	#95	—	2	1	no	—
524	#95	—	2	1	no	—
525	#95	—	2	1	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	2	no	—
529	#95	—	2	2	no	—
530	C₁₉	#25565	1	1	yes	characteristic, direct product factor, Sylow
531	C₂⁴	—	2	2	no	—
532	C₂⁴	—	2	1	no	—
533	C₂⁴	—	2	1	no	—
534	C₂⁴	—	4	2	no	—
535	C₂⁴	—	8	1	no	—
536	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
537	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
538	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
539	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
540	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
541	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
542	#41	—	8	2	no	—
543	#41	—	8	2	no	—
544	C₂×Q₈	—	2	1	no	—
545	C₂×Q₈	—	2	1	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	1	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	8	2	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	4	no	—
580	C₂²×C₄	—	8	1	no	—
581	C₂²×C₄	—	8	1	no	—
582	C₂²×C₄	—	8	2	no	—
583	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
584	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
586	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
589	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	4	4	no	—
599	C₄⋊C₄	—	8	2	no	—
600	C₄⋊C₄	—	8	1	no	—
601	C₄⋊C₄	—	8	1	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	2	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	4	4	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	2	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	1	no	—
627	C₂²⋊C₄	—	4	1	no	—
628	C₂²⋊C₄	—	8	1	no	—
629	C₂²⋊C₄	—	8	2	no	—
630	C₂²⋊C₄	#41×C₁₉	1	4	yes	complemented
631	C₄²	—	2	2	no	—
632	C₄²	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	4	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	2	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	—	8	4	no	—
657	C₂³	—	8	2	no	—
658	C₂³	—	8	2	no	—
659	C₂³	C₁₉×#120	1	2	yes	—
660	C₂³	C₁₉×#120	1	1	yes	characteristic
661	C₂³	C₁₉×#120	1	1	yes	characteristic
662	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
663	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
664	C₂³	C₂×#41×C₁₉	1	2	yes	—
665	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂³	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
667	Q₈	—	8	1	no	—
668	Q₈	—	8	1	no	—
669	D₄	—	4	4	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	2	no	—
673	D₄	—	4	2	no	—
674	D₄	—	4	2	no	—
675	D₄	—	8	2	no	—
676	D₄	—	8	2	no	—
677	D₄	—	8	1	no	—
678	D₄	—	8	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	2	no	—
704	C₂×C₄	—	4	2	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	8	1	no	—
719	C₂×C₄	—	8	1	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	2	no	—
722	C₂×C₄	—	8	8	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	1	no	—
737	C₂²	—	4	1	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	4	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	8	2	no	—
746	C₂²	—	8	1	no	—
747	C₂²	—	8	1	no	—
748	C₂²	—	8	2	no	—
749	C₂²	—	8	2	no	—
750	C₂²	—	8	2	no	—
751	C₂²	C₁₉×#458	1	2	yes	—
752	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
753	C₂²	C₁₉×#532	1	1	yes	characteristic
754	C₂²	C₁₉×#537	1	1	yes	characteristic
755	C₂²	C₁₉×#546	1	2	yes	—
756	C₂²	C₁₉×#547	1	2	yes	—
757	C₄	—	4	4	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	1	no	—
764	C₄	—	4	2	no	—
765	C₄	—	8	2	no	—
766	C₄	—	8	1	no	—
767	C₄	—	8	1	no	—
768	C₄	—	8	1	no	—
769	C₄	—	8	1	no	—
770	C₂	—	2	2	no	—
771	C₂	—	2	1	no	—
772	C₂	—	2	1	no	—
773	C₂	—	2	2	no	—
774	C₂	—	2	2	no	—
775	C₂	—	4	1	no	—
776	C₂	—	4	2	no	—
777	C₂	—	8	2	no	—
778	C₂	C₁₉×#2430	1	1	yes	characteristic
779	C₂	C₂×C₁₉×#458	1	1	yes	characteristic
780	C₂	C₁₉×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₁₉×#3490	C₂
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂⁵×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2483	C₂	semidirect
3. C₁₉×#2412	C₂	semidirect
4. C₁₉×#2062	C₂	semidirect
5. C₁₉×#2044	C₂	semidirect
6. C₁₉×#2030	C₂	semidirect
7. C₁₉×#2022	C₂	semidirect
8. C₁₉×#1898	C₂	semidirect
9. C₁₉×#1890	C₂	semidirect
10. C₁₉×#1867	C₂	semidirect
11. C₂×C₁₉×#342	C₂	semidirect
239. C₂²⋊C₄×C₁₉	#41	semidirect
242. #25565	C₁₉	direct (N × H)
334. #2483	C₂×C₁₉	semidirect
335. #2412	C₂×C₁₉	semidirect
336. #2062	C₂×C₁₉	semidirect
337. #2044	C₂×C₁₉	semidirect
338. #2030	C₂×C₁₉	semidirect
339. #2022	C₂×C₁₉	semidirect
340. #1898	C₂×C₁₉	semidirect
341. #1890	C₂×C₁₉	semidirect
342. #1867	C₂×C₁₉	semidirect
343. C₂×#342	C₂×C₁₉	semidirect
530. C₁₉	#25565	direct (N × H)
630. C₂²⋊C₄	#41×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×#3490	2
C₁₉×#2483	2
C₁₉×#2412	2
C₁₉×#2062	2
C₁₉×#2044	2
C₁₉×#2030	2
C₁₉×#2022	2
C₁₉×#1898	2
C₁₉×#1890	2
C₁₉×#1867	2
C₂×C₁₉×#342	2
#25565	19

Subgroups — C19×#25565 #18031524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#25565 #18031524