Subgroups — C₂×C₁₉×#2427 #18040656

Order 4864.

3894 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₉×#121	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2427	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₉×#397	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#394	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₉×#386	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₉×#380	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉×#124	—	2	8	no	—
19	C₂×C₁₉×#124	C₂²	1	8	yes	complemented
20	C₂×C₁₉×C₂²⋊Q₈	—	2	8	no	—
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	8	yes	complemented
22	C₂×C₁₉×#121	—	2	8	no	—
23	C₂×C₁₉×#121	C₂²	1	8	yes	—
24	C₂×C₄×D₄×C₁₉	—	2	8	no	—
25	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
26	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
34	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#397	C₂²	1	16	yes	complemented
40	C₁₉×#394	C₂²	1	16	yes	complemented
41	C₁₉×#391	C₂²	1	8	yes	complemented
42	C₁₉×#389	C₂²	1	8	yes	complemented
43	C₁₉×#386	C₂²	1	16	yes	complemented
44	C₁₉×#380	C₂²	1	16	yes	complemented
45	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	complemented
46	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
47	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
48	C₂×C₁₉×#95	C₂²	1	2	yes	—
49	C₂×C₁₉×#95	C₂²	1	2	yes	—
50	C₂×C₁₉×#95	C₂²	1	2	yes	—
51	C₂⁵×C₁₉	C₂³	1	2	yes	—
52	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₉	—	2	4	no	—
54	C₂²×Q₈×C₁₉	—	2	4	no	—
55	C₂²×Q₈×C₁₉	—	2	4	no	—
56	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₉	—	2	8	no	—
58	C₂²×D₄×C₁₉	—	2	8	no	—
59	C₂²×D₄×C₁₉	—	2	4	no	—
60	C₂²×D₄×C₁₉	—	2	4	no	—
61	C₂²×D₄×C₁₉	—	4	4	no	—
62	C₂²×D₄×C₁₉	D₄	1	8	yes	—
63	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
64	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₉	—	2	8	no	—
66	C₂³×C₄×C₁₉	—	2	4	no	—
67	C₂³×C₄×C₁₉	—	2	4	no	—
68	C₂³×C₄×C₁₉	—	2	8	no	—
69	C₂³×C₄×C₁₉	—	2	4	no	—
70	C₂³×C₄×C₁₉	—	4	4	no	—
71	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
79	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₁₉×#124	—	2	32	no	—
83	C₁₉×C₂²⋊Q₈	—	2	32	no	—
84	C₁₉×#121	—	2	32	no	—
85	C₄×D₄×C₁₉	—	2	32	no	—
86	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
88	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
89	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	complemented
90	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
91	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
95	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
96	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
97	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
99	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
100	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
101	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
106	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
108	C₂×C₄²×C₁₉	—	2	4	no	—
109	C₂×C₄²×C₁₉	—	2	4	no	—
110	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
111	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
112	C₁₉×#95	C₂³	1	4	yes	—
113	C₁₉×#95	C₂³	1	4	yes	—
114	C₁₉×#95	C₂³	1	8	yes	—
115	C₁₉×#95	C₂³	1	8	yes	—
116	C₁₉×#95	C₂³	1	8	yes	—
117	C₂⁴×C₁₉	—	2	2	no	—
118	C₂⁴×C₁₉	—	2	4	no	—
119	C₂⁴×C₁₉	—	2	2	no	—
120	C₂⁴×C₁₉	—	2	2	no	—
121	C₂⁴×C₁₉	—	2	2	no	—
122	C₂⁴×C₁₉	—	2	4	no	—
123	C₂⁴×C₁₉	—	2	4	no	—
124	C₂⁴×C₁₉	—	2	4	no	—
125	C₂⁴×C₁₉	—	2	4	no	—
126	C₂⁴×C₁₉	—	2	2	no	—
127	C₂⁴×C₁₉	—	2	4	no	—
128	C₂⁴×C₁₉	—	2	2	no	—
129	C₂⁴×C₁₉	C₂×D₄	1	8	yes	—
130	C₂⁴×C₁₉	#41	1	4	yes	—
131	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
132	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
133	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
134	C₂×Q₈×C₁₉	—	2	8	no	—
135	C₂×Q₈×C₁₉	—	2	8	no	—
136	C₂×Q₈×C₁₉	—	2	8	no	—
137	C₂×Q₈×C₁₉	—	4	16	no	—
138	C₂×D₄×C₁₉	—	2	16	no	—
139	C₂×D₄×C₁₉	—	2	16	no	—
140	C₂×D₄×C₁₉	—	2	32	no	—
141	C₂×D₄×C₁₉	—	2	8	no	—
142	C₂×D₄×C₁₉	—	2	8	no	—
143	C₂×D₄×C₁₉	—	4	8	no	—
144	C₂×D₄×C₁₉	—	4	32	no	—
145	C₂×D₄×C₁₉	C₂×D₄	1	16	yes	—
146	C₂²×C₄×C₁₉	—	2	2	no	—
147	C₂²×C₄×C₁₉	—	2	4	no	—
148	C₂²×C₄×C₁₉	—	2	4	no	—
149	C₂²×C₄×C₁₉	—	2	2	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	4	no	—
155	C₂²×C₄×C₁₉	—	2	4	no	—
156	C₂²×C₄×C₁₉	—	2	4	no	—
157	C₂²×C₄×C₁₉	—	2	2	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	2	no	—
160	C₂²×C₄×C₁₉	—	2	2	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	2	4	no	—
163	C₂²×C₄×C₁₉	—	2	4	no	—
164	C₂²×C₄×C₁₉	—	2	2	no	—
165	C₂²×C₄×C₁₉	—	2	4	no	—
166	C₂²×C₄×C₁₉	—	2	2	no	—
167	C₂²×C₄×C₁₉	—	2	2	no	—
168	C₂²×C₄×C₁₉	—	2	16	no	—
169	C₂²×C₄×C₁₉	—	2	8	no	—
170	C₂²×C₄×C₁₉	—	2	8	no	—
171	C₂²×C₄×C₁₉	—	2	16	no	—
172	C₂²×C₄×C₁₉	—	2	8	no	—
173	C₂²×C₄×C₁₉	—	4	8	no	—
174	C₂²×C₄×C₁₉	—	4	32	no	—
175	C₂²×C₄×C₁₉	—	4	16	no	—
176	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
177	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₁₉	#41	1	4	yes	—
180	C₂²×C₄×C₁₉	#41	1	4	yes	—
181	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
190	C₄⋊C₄×C₁₉	—	2	8	no	—
191	C₄⋊C₄×C₁₉	—	2	16	no	—
192	C₄⋊C₄×C₁₉	—	4	8	no	—
193	C₄⋊C₄×C₁₉	C₂×D₄	1	16	yes	complemented
194	C₂²⋊C₄×C₁₉	—	2	16	no	—
195	C₂²⋊C₄×C₁₉	—	2	16	no	—
196	C₂²⋊C₄×C₁₉	—	2	16	no	—
197	C₂²⋊C₄×C₁₉	—	2	8	no	—
198	C₂²⋊C₄×C₁₉	—	2	16	no	—
199	C₂²⋊C₄×C₁₉	—	2	16	no	—
200	C₂²⋊C₄×C₁₉	—	2	8	no	—
201	C₄²×C₁₉	—	2	8	no	—
202	C₄²×C₁₉	—	2	8	no	—
203	C₂×#2427	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂³×C₁₉	—	2	16	no	—
205	C₂³×C₁₉	—	2	8	no	—
206	C₂³×C₁₉	—	2	8	no	—
207	C₂³×C₁₉	—	2	16	no	—
208	C₂³×C₁₉	—	2	16	no	—
209	C₂³×C₁₉	—	2	8	no	—
210	C₂³×C₁₉	—	2	2	no	—
211	C₂³×C₁₉	—	2	4	no	—
212	C₂³×C₁₉	—	2	2	no	—
213	C₂³×C₁₉	—	2	2	no	—
214	C₂³×C₁₉	—	2	2	no	—
215	C₂³×C₁₉	—	2	4	no	—
216	C₂³×C₁₉	—	2	4	no	—
217	C₂³×C₁₉	—	2	4	no	—
218	C₂³×C₁₉	—	2	4	no	—
219	C₂³×C₁₉	—	2	2	no	—
220	C₂³×C₁₉	—	2	4	no	—
221	C₂³×C₁₉	—	2	2	no	—
222	C₂³×C₁₉	—	4	4	no	—
223	C₂³×C₁₉	—	4	8	no	—
224	C₂³×C₁₉	—	4	4	no	—
225	C₂³×C₁₉	—	4	8	no	—
226	C₂³×C₁₉	—	4	8	no	—
227	C₂³×C₁₉	—	4	4	no	—
228	C₂³×C₁₉	—	4	4	no	—
229	C₂³×C₁₉	—	4	8	no	—
230	C₂³×C₁₉	C₂²×D₄	1	8	yes	—
231	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
232	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
233	C₂³×C₁₉	C₂×#41	1	4	yes	—
234	C₂³×C₁₉	C₂×#41	1	2	yes	—
235	C₂³×C₁₉	C₂×#41	1	2	yes	—
236	C₂³×C₁₉	C₂×#41	1	2	yes	—
237	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
238	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
239	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
240	Q₈×C₁₉	—	4	16	no	—
241	D₄×C₁₉	—	2	32	no	—
242	D₄×C₁₉	—	4	32	no	—
243	C₂×C₄×C₁₉	—	2	8	no	—
244	C₂×C₄×C₁₉	—	2	16	no	—
245	C₂×C₄×C₁₉	—	2	2	no	—
246	C₂×C₄×C₁₉	—	2	4	no	—
247	C₂×C₄×C₁₉	—	2	4	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	2	no	—
250	C₂×C₄×C₁₉	—	2	2	no	—
251	C₂×C₄×C₁₉	—	2	2	no	—
252	C₂×C₄×C₁₉	—	2	2	no	—
253	C₂×C₄×C₁₉	—	2	4	no	—
254	C₂×C₄×C₁₉	—	2	4	no	—
255	C₂×C₄×C₁₉	—	2	4	no	—
256	C₂×C₄×C₁₉	—	2	2	no	—
257	C₂×C₄×C₁₉	—	2	2	no	—
258	C₂×C₄×C₁₉	—	2	2	no	—
259	C₂×C₄×C₁₉	—	2	2	no	—
260	C₂×C₄×C₁₉	—	2	2	no	—
261	C₂×C₄×C₁₉	—	2	4	no	—
262	C₂×C₄×C₁₉	—	2	4	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	4	no	—
265	C₂×C₄×C₁₉	—	2	2	no	—
266	C₂×C₄×C₁₉	—	2	2	no	—
267	C₂×C₄×C₁₉	—	4	32	no	—
268	C₂×C₄×C₁₉	—	4	4	no	—
269	C₂×C₄×C₁₉	—	4	8	no	—
270	C₂×C₄×C₁₉	—	4	4	no	—
271	C₂×C₄×C₁₉	—	4	8	no	—
272	C₂×C₄×C₁₉	—	4	4	no	—
273	C₂×C₄×C₁₉	—	4	4	no	—
274	C₂×C₄×C₁₉	—	4	16	no	—
275	C₂×C₄×C₁₉	#121	1	16	yes	—
276	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
277	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
280	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
281	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic, complemented
282	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic, complemented
283	C₂²×#121	C₂×C₁₉	1	1	yes	characteristic
284	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
285	#2427	C₂×C₁₉	1	16	yes	direct product factor
286	C₂×#397	C₂×C₁₉	1	2	yes	complemented
287	C₂×#394	C₂×C₁₉	1	2	yes	complemented
288	C₂×#391	C₂×C₁₉	1	1	yes	characteristic, complemented
289	C₂×#389	C₂×C₁₉	1	1	yes	characteristic, complemented
290	C₂×#386	C₂×C₁₉	1	2	yes	complemented
291	C₂×#380	C₂×C₁₉	1	2	yes	complemented
292	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
293	C₂²×C₁₉	—	2	8	no	—
294	C₂²×C₁₉	—	2	4	no	—
295	C₂²×C₁₉	—	2	4	no	—
296	C₂²×C₁₉	—	2	8	no	—
297	C₂²×C₁₉	—	2	8	no	—
298	C₂²×C₁₉	—	2	4	no	—
299	C₂²×C₁₉	—	4	2	no	—
300	C₂²×C₁₉	—	4	4	no	—
301	C₂²×C₁₉	—	4	32	no	—
302	C₂²×C₁₉	—	4	16	no	—
303	C₂²×C₁₉	—	4	2	no	—
304	C₂²×C₁₉	—	4	4	no	—
305	C₂²×C₁₉	—	4	4	no	—
306	C₂²×C₁₉	—	4	2	no	—
307	C₂²×C₁₉	—	4	2	no	—
308	C₂²×C₁₉	—	4	4	no	—
309	C₂²×C₁₉	C₂×#121	1	4	yes	—
310	C₂²×C₁₉	#529	1	4	yes	—
311	C₂²×C₁₉	#542	1	4	yes	—
312	C₂²×C₁₉	#546	1	4	yes	—
313	C₂²×C₁₉	#546	1	4	yes	—
314	C₂²×C₁₉	#547	1	4	yes	—
315	C₂²×C₁₉	#548	1	4	yes	—
316	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
317	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
318	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
319	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
320	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
321	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
322	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
323	C₄×C₁₉	—	2	4	no	—
324	C₄×C₁₉	—	2	8	no	—
325	C₄×C₁₉	—	4	2	no	—
326	C₄×C₁₉	—	4	4	no	—
327	C₄×C₁₉	—	4	2	no	—
328	C₄×C₁₉	—	4	4	no	—
329	C₄×C₁₉	—	4	2	no	—
330	C₄×C₁₉	—	4	2	no	—
331	C₄×C₁₉	C₂×#121	1	8	yes	—
332	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
333	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
334	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
335	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
336	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
337	C₂×#124	—	2	8	no	—
338	C₂×#124	C₂²×C₁₉	1	8	yes	complemented
339	C₂×C₂²⋊Q₈	—	2	8	no	—
340	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	8	yes	complemented
341	C₂×#121	—	2	8	no	—
342	C₂×#121	C₂²×C₁₉	1	8	yes	—
343	C₂×C₄×D₄	—	2	8	no	—
344	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
345	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
346	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
347	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
348	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
350	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
351	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
352	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
353	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
354	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
355	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
356	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
357	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
358	#397	C₂²×C₁₉	1	16	yes	complemented
359	#394	C₂²×C₁₉	1	16	yes	complemented
360	#391	C₂²×C₁₉	1	8	yes	complemented
361	#389	C₂²×C₁₉	1	8	yes	complemented
362	#386	C₂²×C₁₉	1	16	yes	complemented
363	#380	C₂²×C₁₉	1	16	yes	complemented
364	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	complemented
365	C₂×#95	C₂²×C₁₉	1	2	yes	—
366	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
367	C₂×#95	C₂²×C₁₉	1	2	yes	—
368	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
369	C₂×#95	C₂²×C₁₉	1	2	yes	—
370	C₂×C₁₉	—	4	8	no	—
371	C₂×C₁₉	—	4	4	no	—
372	C₂×C₁₉	#2427	1	8	yes	direct product factor
373	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
374	C₂×C₁₉	C₂×#529	1	1	yes	characteristic
375	C₂×C₁₉	C₂×#542	1	1	yes	characteristic
376	C₂×C₁₉	C₂×#546	1	1	yes	characteristic
377	C₂×C₁₉	C₂×#546	1	1	yes	characteristic
378	C₂×C₁₉	C₂×#547	1	1	yes	characteristic
379	C₂×C₁₉	C₂×#548	1	1	yes	characteristic
380	C₂⁵	C₂³×C₁₉	1	2	yes	—
381	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
382	C₂²×Q₈	—	2	4	no	—
383	C₂²×Q₈	—	2	4	no	—
384	C₂²×Q₈	—	2	4	no	—
385	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
386	C₂²×D₄	—	2	8	no	—
387	C₂²×D₄	—	2	8	no	—
388	C₂²×D₄	—	2	4	no	—
389	C₂²×D₄	—	2	4	no	—
390	C₂²×D₄	—	4	4	no	—
391	C₂²×D₄	D₄×C₁₉	1	8	yes	—
392	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
393	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
394	C₂³×C₄	—	2	8	no	—
395	C₂³×C₄	—	2	4	no	—
396	C₂³×C₄	—	2	4	no	—
397	C₂³×C₄	—	2	8	no	—
398	C₂³×C₄	—	2	4	no	—
399	C₂³×C₄	—	4	4	no	—
400	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
402	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
404	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
405	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
406	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
407	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
408	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
409	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
411	#124	—	2	32	no	—
412	C₂²⋊Q₈	—	2	32	no	—
413	#121	—	2	32	no	—
414	C₄×D₄	—	2	32	no	—
415	C₂×C₄⋊C₄	—	2	4	no	—
416	C₂×C₄⋊C₄	—	2	8	no	—
417	C₂×C₄⋊C₄	—	4	4	no	—
418	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	complemented
419	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
421	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
422	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
423	C₂×C₂²⋊C₄	—	2	8	no	—
424	C₂×C₂²⋊C₄	—	2	8	no	—
425	C₂×C₂²⋊C₄	—	2	8	no	—
426	C₂×C₂²⋊C₄	—	2	4	no	—
427	C₂×C₂²⋊C₄	—	2	8	no	—
428	C₂×C₂²⋊C₄	—	2	8	no	—
429	C₂×C₂²⋊C₄	—	2	4	no	—
430	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
437	C₂×C₄²	—	2	4	no	—
438	C₂×C₄²	—	2	4	no	—
439	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
440	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
441	#95	C₂³×C₁₉	1	4	yes	—
442	#95	C₂³×C₁₉	1	4	yes	—
443	#95	C₂³×C₁₉	1	8	yes	—
444	#95	C₂³×C₁₉	1	8	yes	—
445	#95	C₂³×C₁₉	1	8	yes	—
446	C₁₉	C₂×#2427	1	1	yes	characteristic, direct product factor, Sylow
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	—	2	2	no	—
451	C₂⁴	—	2	2	no	—
452	C₂⁴	—	2	4	no	—
453	C₂⁴	—	2	4	no	—
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	2	4	no	—
456	C₂⁴	—	2	2	no	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	—	2	2	no	—
459	C₂⁴	C₂×D₄×C₁₉	1	8	yes	—
460	C₂⁴	#41×C₁₉	1	4	yes	—
461	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
462	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
463	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
464	C₂×Q₈	—	2	8	no	—
465	C₂×Q₈	—	2	8	no	—
466	C₂×Q₈	—	2	8	no	—
467	C₂×Q₈	—	4	16	no	—
468	C₂×D₄	—	2	16	no	—
469	C₂×D₄	—	2	16	no	—
470	C₂×D₄	—	2	32	no	—
471	C₂×D₄	—	2	8	no	—
472	C₂×D₄	—	2	8	no	—
473	C₂×D₄	—	4	8	no	—
474	C₂×D₄	—	4	32	no	—
475	C₂×D₄	C₂×D₄×C₁₉	1	16	yes	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	16	no	—
499	C₂²×C₄	—	2	8	no	—
500	C₂²×C₄	—	2	8	no	—
501	C₂²×C₄	—	2	16	no	—
502	C₂²×C₄	—	2	8	no	—
503	C₂²×C₄	—	4	8	no	—
504	C₂²×C₄	—	4	32	no	—
505	C₂²×C₄	—	4	16	no	—
506	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
507	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
508	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
509	C₂²×C₄	#41×C₁₉	1	4	yes	—
510	C₂²×C₄	#41×C₁₉	1	4	yes	—
511	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
513	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
514	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
516	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
517	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
518	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
520	C₄⋊C₄	—	2	8	no	—
521	C₄⋊C₄	—	2	16	no	—
522	C₄⋊C₄	—	4	8	no	—
523	C₄⋊C₄	C₂×D₄×C₁₉	1	16	yes	complemented
524	C₂²⋊C₄	—	2	16	no	—
525	C₂²⋊C₄	—	2	16	no	—
526	C₂²⋊C₄	—	2	16	no	—
527	C₂²⋊C₄	—	2	8	no	—
528	C₂²⋊C₄	—	2	16	no	—
529	C₂²⋊C₄	—	2	16	no	—
530	C₂²⋊C₄	—	2	8	no	—
531	C₄²	—	2	8	no	—
532	C₄²	—	2	8	no	—
533	C₂³	—	2	16	no	—
534	C₂³	—	2	8	no	—
535	C₂³	—	2	8	no	—
536	C₂³	—	2	16	no	—
537	C₂³	—	2	16	no	—
538	C₂³	—	2	8	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	4	4	no	—
552	C₂³	—	4	8	no	—
553	C₂³	—	4	4	no	—
554	C₂³	—	4	8	no	—
555	C₂³	—	4	8	no	—
556	C₂³	—	4	4	no	—
557	C₂³	—	4	4	no	—
558	C₂³	—	4	8	no	—
559	C₂³	C₂²×D₄×C₁₉	1	8	yes	—
560	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
561	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
562	C₂³	C₂×#41×C₁₉	1	4	yes	—
563	C₂³	C₂×#41×C₁₉	1	2	yes	—
564	C₂³	C₂×#41×C₁₉	1	2	yes	—
565	C₂³	C₂×#41×C₁₉	1	2	yes	—
566	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
567	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
568	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
569	Q₈	—	4	16	no	—
570	D₄	—	2	32	no	—
571	D₄	—	4	32	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	16	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	32	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	8	no	—
599	C₂×C₄	—	4	8	no	—
600	C₂×C₄	—	4	4	no	—
601	C₂×C₄	—	4	4	no	—
602	C₂×C₄	—	4	4	no	—
603	C₂×C₄	—	4	16	no	—
604	C₂×C₄	C₁₉×#121	1	16	yes	—
605	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
606	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
607	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
608	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
609	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	4	no	—
612	C₂²	—	2	4	no	—
613	C₂²	—	2	8	no	—
614	C₂²	—	2	8	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	4	no	—
618	C₂²	—	4	32	no	—
619	C₂²	—	4	16	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	4	no	—
626	C₂²	C₂×C₁₉×#121	1	4	yes	—
627	C₂²	C₁₉×#529	1	4	yes	—
628	C₂²	C₁₉×#542	1	4	yes	—
629	C₂²	C₁₉×#546	1	4	yes	—
630	C₂²	C₁₉×#546	1	4	yes	—
631	C₂²	C₁₉×#547	1	4	yes	—
632	C₂²	C₁₉×#548	1	4	yes	—
633	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
634	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
635	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
636	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
637	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
638	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
639	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
640	C₄	—	2	4	no	—
641	C₄	—	2	8	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	4	no	—
644	C₄	—	4	4	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	2	no	—
648	C₄	C₂×C₁₉×#121	1	8	yes	—
649	C₂	—	4	8	no	—
650	C₂	—	4	4	no	—
651	C₂	C₁₉×#2427	1	8	yes	direct product factor
652	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
653	C₂	C₂×C₁₉×#529	1	1	yes	characteristic
654	C₂	C₂×C₁₉×#542	1	1	yes	characteristic
655	C₂	C₂×C₁₉×#546	1	1	yes	characteristic
656	C₂	C₂×C₁₉×#546	1	1	yes	characteristic
657	C₂	C₂×C₁₉×#547	1	1	yes	characteristic
658	C₂	C₂×C₁₉×#548	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂²×C₁₉×#121	C₂
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
1. C₂²×C₁₉×#124	C₂	semidirect
2. C₂²×C₁₉×C₂²⋊Q₈	C₂	semidirect
4. C₂²×C₄×D₄×C₁₉	C₂	semidirect
5. C₁₉×#2427	C₂	direct (N × H)
6. C₂×C₁₉×#397	C₂	semidirect
7. C₂×C₁₉×#394	C₂	semidirect
8. C₂×C₁₉×#391	C₂	semidirect
9. C₂×C₁₉×#389	C₂	semidirect
10. C₂×C₁₉×#386	C₂	semidirect
11. C₂×C₁₉×#380	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₁₉	C₂	semidirect
19. C₂×C₁₉×#124	C₂²	semidirect
21. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₄×D₄×C₁₉	C₂²	semidirect
39. C₁₉×#397	C₂²	semidirect
40. C₁₉×#394	C₂²	semidirect
41. C₁₉×#391	C₂²	semidirect
42. C₁₉×#389	C₂²	semidirect
43. C₁₉×#386	C₂²	semidirect
44. C₁₉×#380	C₂²	semidirect
45. C₄×C₂²⋊C₄×C₁₉	C₂²	semidirect
89. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
193. C₄⋊C₄×C₁₉	C₂×D₄	semidirect
203. C₂×#2427	C₁₉	direct (N × H)
281. C₂²×#124	C₂×C₁₉	semidirect
282. C₂²×C₂²⋊Q₈	C₂×C₁₉	semidirect
284. C₂²×C₄×D₄	C₂×C₁₉	semidirect
285. #2427	C₂×C₁₉	direct (N × H)
286. C₂×#397	C₂×C₁₉	semidirect
287. C₂×#394	C₂×C₁₉	semidirect
288. C₂×#391	C₂×C₁₉	semidirect
289. C₂×#389	C₂×C₁₉	semidirect
290. C₂×#386	C₂×C₁₉	semidirect
291. C₂×#380	C₂×C₁₉	semidirect
292. C₂×C₄×C₂²⋊C₄	C₂×C₁₉	semidirect
338. C₂×#124	C₂²×C₁₉	semidirect
340. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
344. C₂×C₄×D₄	C₂²×C₁₉	semidirect
358. #397	C₂²×C₁₉	semidirect
359. #394	C₂²×C₁₉	semidirect
360. #391	C₂²×C₁₉	semidirect
361. #389	C₂²×C₁₉	semidirect
362. #386	C₂²×C₁₉	semidirect
363. #380	C₂²×C₁₉	semidirect
364. C₄×C₂²⋊C₄	C₂²×C₁₉	semidirect
372. C₂×C₁₉	#2427	direct (N × H)
418. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
446. C₁₉	C₂×#2427	direct (N × H)
523. C₄⋊C₄	C₂×D₄×C₁₉	semidirect
651. C₂	C₁₉×#2427	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#124	2
C₂²×C₁₉×C₂²⋊Q₈	2
C₂²×C₁₉×#121	2
C₂²×C₄×D₄×C₁₉	2
C₁₉×#2427	2
C₂×C₁₉×#397	2
C₂×C₁₉×#394	2
C₂×C₁₉×#391	2
C₂×C₁₉×#389	2
C₂×C₁₉×#386	2
C₂×C₁₉×#380	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₂×#2427	19

Subgroups — C2×C19×#2427 #18040656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2427 #18040656