Subgroups — C₂×C₁₉×#2535 #18040844

Order 4864.

4390 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#121	C₂	1	2	yes	maximal, complemented
2	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2535	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₉×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#392	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#386	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₉×#380	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	—	2	16	no	—
16	C₂×C₁₉×#121	C₂²	1	16	yes	complemented
17	C₂×C₄×D₄×C₁₉	—	2	8	no	—
18	C₂×C₄×D₄×C₁₉	—	2	8	no	—
19	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
20	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
28	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#397	C₂²	1	16	yes	complemented
30	C₁₉×#392	C₂²	1	16	yes	complemented
31	C₁₉×#386	C₂²	1	32	yes	complemented
32	C₁₉×#382	C₂²	1	8	yes	complemented
33	C₁₉×#380	C₂²	1	16	yes	complemented
34	C₂×C₁₉×#95	C₂²	1	4	yes	—
35	C₂×C₁₉×#95	C₂²	1	2	yes	—
36	C₂×C₁₉×#95	C₂²	1	2	yes	—
37	C₂⁵×C₁₉	C₂³	1	2	yes	—
38	C₂⁵×C₁₉	C₂³	1	2	yes	—
39	C₂²×D₄×C₁₉	—	2	8	no	—
40	C₂²×D₄×C₁₉	—	2	16	no	—
41	C₂²×D₄×C₁₉	—	2	16	no	—
42	C₂²×D₄×C₁₉	—	2	4	no	—
43	C₂²×D₄×C₁₉	—	2	4	no	—
44	C₂²×D₄×C₁₉	—	2	4	no	—
45	C₂²×D₄×C₁₉	—	4	8	no	—
46	C₂²×D₄×C₁₉	D₄	1	8	yes	complemented
47	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
48	C₂²×D₄×C₁₉	C₂³	1	16	yes	—
49	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₉	—	2	8	no	—
51	C₂³×C₄×C₁₉	—	2	8	no	—
52	C₂³×C₄×C₁₉	—	2	8	no	—
53	C₂³×C₄×C₁₉	—	2	8	no	—
54	C₂³×C₄×C₁₉	—	4	8	no	—
55	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
56	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₁₉×#121	—	2	64	no	—
64	C₄×D₄×C₁₉	—	2	32	no	—
65	C₄×D₄×C₁₉	—	2	32	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
80	C₂×C₄²×C₁₉	D₄	1	8	yes	complemented
81	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
82	C₁₉×#95	C₂³	1	16	yes	—
83	C₁₉×#95	C₂³	1	8	yes	—
84	C₁₉×#95	C₂³	1	8	yes	—
85	C₂⁴×C₁₉	—	2	4	no	—
86	C₂⁴×C₁₉	—	2	4	no	—
87	C₂⁴×C₁₉	—	2	4	no	—
88	C₂⁴×C₁₉	—	2	4	no	—
89	C₂⁴×C₁₉	—	2	4	no	—
90	C₂⁴×C₁₉	—	2	4	no	—
91	C₂⁴×C₁₉	—	2	8	no	—
92	C₂⁴×C₁₉	—	2	4	no	—
93	C₂⁴×C₁₉	—	2	8	no	—
94	C₂⁴×C₁₉	—	2	4	no	—
95	C₂⁴×C₁₉	C₂×D₄	1	8	yes	—
96	C₂⁴×C₁₉	#41	1	8	yes	—
97	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
98	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
99	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
100	C₂×D₄×C₁₉	—	2	32	no	—
101	C₂×D₄×C₁₉	—	2	16	no	—
102	C₂×D₄×C₁₉	—	2	32	no	—
103	C₂×D₄×C₁₉	—	2	32	no	—
104	C₂×D₄×C₁₉	—	2	32	no	—
105	C₂×D₄×C₁₉	—	2	8	no	—
106	C₂×D₄×C₁₉	—	2	8	no	—
107	C₂×D₄×C₁₉	—	2	8	no	—
108	C₂×D₄×C₁₉	—	4	16	no	—
109	C₂×D₄×C₁₉	—	4	64	no	—
110	C₂×D₄×C₁₉	C₂×D₄	1	16	yes	complemented
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	4	no	—
116	C₂²×C₄×C₁₉	—	2	8	no	—
117	C₂²×C₄×C₁₉	—	2	4	no	—
118	C₂²×C₄×C₁₉	—	2	8	no	—
119	C₂²×C₄×C₁₉	—	2	8	no	—
120	C₂²×C₄×C₁₉	—	2	8	no	—
121	C₂²×C₄×C₁₉	—	2	16	no	—
122	C₂²×C₄×C₁₉	—	2	16	no	—
123	C₂²×C₄×C₁₉	—	2	16	no	—
124	C₂²×C₄×C₁₉	—	2	16	no	—
125	C₂²×C₄×C₁₉	—	4	16	no	—
126	C₂²×C₄×C₁₉	—	4	32	no	—
127	C₂²×C₄×C₁₉	—	4	32	no	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₉	#41	1	4	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
139	C₄⋊C₄×C₁₉	—	2	8	no	—
140	C₄⋊C₄×C₁₉	—	2	8	no	—
141	C₄⋊C₄×C₁₉	—	2	16	no	—
142	C₂²⋊C₄×C₁₉	—	2	32	no	—
143	C₂²⋊C₄×C₁₉	—	2	16	no	—
144	C₂²⋊C₄×C₁₉	—	2	16	no	—
145	C₂²⋊C₄×C₁₉	—	4	16	no	—
146	C₄²×C₁₉	C₂×D₄	1	16	yes	complemented
147	C₂×#2535	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	2	16	no	—
149	C₂³×C₁₉	—	2	16	no	—
150	C₂³×C₁₉	—	2	16	no	—
151	C₂³×C₁₉	—	2	32	no	—
152	C₂³×C₁₉	—	2	16	no	—
153	C₂³×C₁₉	—	2	4	no	—
154	C₂³×C₁₉	—	2	4	no	—
155	C₂³×C₁₉	—	2	4	no	—
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	2	4	no	—
158	C₂³×C₁₉	—	2	4	no	—
159	C₂³×C₁₉	—	2	8	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	2	8	no	—
162	C₂³×C₁₉	—	2	4	no	—
163	C₂³×C₁₉	—	4	8	no	—
164	C₂³×C₁₉	—	4	8	no	—
165	C₂³×C₁₉	—	4	8	no	—
166	C₂³×C₁₉	—	4	8	no	—
167	C₂³×C₁₉	—	4	8	no	—
168	C₂³×C₁₉	—	4	8	no	—
169	C₂³×C₁₉	—	4	16	no	—
170	C₂³×C₁₉	C₂²×D₄	1	8	yes	—
171	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
172	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
173	C₂³×C₁₉	C₂×#41	1	8	yes	—
174	C₂³×C₁₉	C₂×#41	1	2	yes	—
175	C₂³×C₁₉	C₂×#41	1	4	yes	—
176	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
177	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
178	D₄×C₁₉	—	2	32	no	—
179	D₄×C₁₉	—	2	32	no	—
180	D₄×C₁₉	—	4	64	no	—
181	C₂×C₄×C₁₉	—	2	8	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	2	4	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	4	no	—
188	C₂×C₄×C₁₉	—	2	8	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	8	no	—
191	C₂×C₄×C₁₉	—	2	8	no	—
192	C₂×C₄×C₁₉	—	2	8	no	—
193	C₂×C₄×C₁₉	—	4	32	no	—
194	C₂×C₄×C₁₉	—	4	8	no	—
195	C₂×C₄×C₁₉	—	4	8	no	—
196	C₂×C₄×C₁₉	—	4	16	no	—
197	C₂×C₄×C₁₉	—	4	32	no	—
198	C₂×C₄×C₁₉	#121	1	16	yes	—
199	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
204	C₂²×#121	C₂×C₁₉	1	2	yes	complemented
205	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
206	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#2535	C₂×C₁₉	1	16	yes	direct product factor
208	C₂×#397	C₂×C₁₉	1	2	yes	complemented
209	C₂×#392	C₂×C₁₉	1	2	yes	complemented
210	C₂×#386	C₂×C₁₉	1	4	yes	complemented
211	C₂×#382	C₂×C₁₉	1	1	yes	characteristic, complemented
212	C₂×#380	C₂×C₁₉	1	2	yes	complemented
213	C₂²×C₁₉	—	2	8	no	—
214	C₂²×C₁₉	—	2	8	no	—
215	C₂²×C₁₉	—	2	8	no	—
216	C₂²×C₁₉	—	2	16	no	—
217	C₂²×C₁₉	—	2	8	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	4	4	no	—
220	C₂²×C₁₉	—	4	4	no	—
221	C₂²×C₁₉	—	4	4	no	—
222	C₂²×C₁₉	—	4	4	no	—
223	C₂²×C₁₉	—	4	4	no	—
224	C₂²×C₁₉	—	4	8	no	—
225	C₂²×C₁₉	—	4	32	no	—
226	C₂²×C₁₉	—	4	32	no	—
227	C₂²×C₁₉	C₂×#121	1	4	yes	—
228	C₂²×C₁₉	#525	1	4	yes	—
229	C₂²×C₁₉	#535	1	4	yes	—
230	C₂²×C₁₉	#546	1	8	yes	—
231	C₂²×C₁₉	#553	1	8	yes	—
232	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
233	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
234	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
235	C₂²×C₁₉	C₂²×#41	1	2	yes	—
236	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
237	C₄×C₁₉	—	2	4	no	—
238	C₄×C₁₉	—	2	4	no	—
239	C₄×C₁₉	—	4	4	no	—
240	C₄×C₁₉	—	4	4	no	—
241	C₄×C₁₉	—	4	8	no	—
242	C₄×C₁₉	C₂×#121	1	8	yes	—
243	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
244	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
245	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
246	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
247	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
248	C₂×#121	—	2	16	no	—
249	C₂×#121	C₂²×C₁₉	1	16	yes	complemented
250	C₂×C₄×D₄	—	2	8	no	—
251	C₂×C₄×D₄	—	2	8	no	—
252	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
253	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
254	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
257	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
258	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
259	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
260	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
261	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
262	#397	C₂²×C₁₉	1	16	yes	complemented
263	#392	C₂²×C₁₉	1	16	yes	complemented
264	#386	C₂²×C₁₉	1	32	yes	complemented
265	#382	C₂²×C₁₉	1	8	yes	complemented
266	#380	C₂²×C₁₉	1	16	yes	complemented
267	C₂×#95	C₂²×C₁₉	1	2	yes	—
268	C₂×#95	C₂²×C₁₉	1	4	yes	—
269	C₂×#95	C₂²×C₁₉	1	2	yes	—
270	C₂×C₁₉	—	4	8	no	—
271	C₂×C₁₉	—	4	8	no	—
272	C₂×C₁₉	#2535	1	8	yes	direct product factor
273	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
274	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
275	C₂×C₁₉	C₂×#535	1	1	yes	characteristic
276	C₂×C₁₉	C₂×#546	1	2	yes	—
277	C₂×C₁₉	C₂×#553	1	2	yes	—
278	C₂⁵	C₂³×C₁₉	1	2	yes	—
279	C₂⁵	C₂³×C₁₉	1	2	yes	—
280	C₂²×D₄	—	2	8	no	—
281	C₂²×D₄	—	2	16	no	—
282	C₂²×D₄	—	2	16	no	—
283	C₂²×D₄	—	2	4	no	—
284	C₂²×D₄	—	2	4	no	—
285	C₂²×D₄	—	2	4	no	—
286	C₂²×D₄	—	4	8	no	—
287	C₂²×D₄	D₄×C₁₉	1	8	yes	complemented
288	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
289	C₂²×D₄	C₂³×C₁₉	1	16	yes	—
290	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
291	C₂³×C₄	—	2	8	no	—
292	C₂³×C₄	—	2	8	no	—
293	C₂³×C₄	—	2	8	no	—
294	C₂³×C₄	—	2	8	no	—
295	C₂³×C₄	—	4	8	no	—
296	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
297	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
299	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
300	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
303	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
304	#121	—	2	64	no	—
305	C₄×D₄	—	2	32	no	—
306	C₄×D₄	—	2	32	no	—
307	C₂×C₄⋊C₄	—	2	4	no	—
308	C₂×C₄⋊C₄	—	2	4	no	—
309	C₂×C₄⋊C₄	—	2	8	no	—
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
311	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
312	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
313	C₂×C₂²⋊C₄	—	2	16	no	—
314	C₂×C₂²⋊C₄	—	2	8	no	—
315	C₂×C₂²⋊C₄	—	2	8	no	—
316	C₂×C₂²⋊C₄	—	4	8	no	—
317	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
321	C₂×C₄²	D₄×C₁₉	1	8	yes	complemented
322	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
323	#95	C₂³×C₁₉	1	16	yes	—
324	#95	C₂³×C₁₉	1	8	yes	—
325	#95	C₂³×C₁₉	1	8	yes	—
326	C₁₉	C₂×#2535	1	1	yes	characteristic, direct product factor, Sylow
327	C₂⁴	—	2	4	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	2	4	no	—
332	C₂⁴	—	2	4	no	—
333	C₂⁴	—	2	8	no	—
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	8	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	C₂×D₄×C₁₉	1	8	yes	—
338	C₂⁴	#41×C₁₉	1	8	yes	—
339	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
340	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
341	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
342	C₂×D₄	—	2	32	no	—
343	C₂×D₄	—	2	16	no	—
344	C₂×D₄	—	2	32	no	—
345	C₂×D₄	—	2	32	no	—
346	C₂×D₄	—	2	32	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	4	16	no	—
351	C₂×D₄	—	4	64	no	—
352	C₂×D₄	C₂×D₄×C₁₉	1	16	yes	complemented
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	16	no	—
364	C₂²×C₄	—	2	16	no	—
365	C₂²×C₄	—	2	16	no	—
366	C₂²×C₄	—	2	16	no	—
367	C₂²×C₄	—	4	16	no	—
368	C₂²×C₄	—	4	32	no	—
369	C₂²×C₄	—	4	32	no	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
372	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
373	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
374	C₂²×C₄	#41×C₁₉	1	4	yes	—
375	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
376	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	16	no	—
384	C₂²⋊C₄	—	2	32	no	—
385	C₂²⋊C₄	—	2	16	no	—
386	C₂²⋊C₄	—	2	16	no	—
387	C₂²⋊C₄	—	4	16	no	—
388	C₄²	C₂×D₄×C₁₉	1	16	yes	complemented
389	C₂³	—	2	16	no	—
390	C₂³	—	2	16	no	—
391	C₂³	—	2	16	no	—
392	C₂³	—	2	32	no	—
393	C₂³	—	2	16	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	8	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	8	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	8	no	—
405	C₂³	—	4	8	no	—
406	C₂³	—	4	8	no	—
407	C₂³	—	4	8	no	—
408	C₂³	—	4	8	no	—
409	C₂³	—	4	8	no	—
410	C₂³	—	4	16	no	—
411	C₂³	C₂²×D₄×C₁₉	1	8	yes	—
412	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
413	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
414	C₂³	C₂×#41×C₁₉	1	8	yes	—
415	C₂³	C₂×#41×C₁₉	1	2	yes	—
416	C₂³	C₂×#41×C₁₉	1	4	yes	—
417	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
418	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
419	D₄	—	2	32	no	—
420	D₄	—	2	32	no	—
421	D₄	—	4	64	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	4	32	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	16	no	—
438	C₂×C₄	—	4	32	no	—
439	C₂×C₄	C₁₉×#121	1	16	yes	—
440	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
441	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
442	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
443	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
444	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
445	C₂²	—	2	8	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	2	8	no	—
448	C₂²	—	2	16	no	—
449	C₂²	—	2	8	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	8	no	—
457	C₂²	—	4	32	no	—
458	C₂²	—	4	32	no	—
459	C₂²	C₂×C₁₉×#121	1	4	yes	—
460	C₂²	C₁₉×#525	1	4	yes	—
461	C₂²	C₁₉×#535	1	4	yes	—
462	C₂²	C₁₉×#546	1	8	yes	—
463	C₂²	C₁₉×#553	1	8	yes	—
464	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
465	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
466	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
467	C₂²	C₂²×#41×C₁₉	1	2	yes	—
468	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
469	C₄	—	2	4	no	—
470	C₄	—	2	4	no	—
471	C₄	—	4	4	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	8	no	—
474	C₄	C₂×C₁₉×#121	1	8	yes	—
475	C₂	—	4	8	no	—
476	C₂	—	4	8	no	—
477	C₂	C₁₉×#2535	1	8	yes	direct product factor
478	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
479	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
480	C₂	C₂×C₁₉×#535	1	1	yes	characteristic
481	C₂	C₂×C₁₉×#546	1	2	yes	—
482	C₂	C₂×C₁₉×#553	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
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×#121	C₂	semidirect
2. C₂²×C₄×D₄×C₁₉	C₂	semidirect
3. C₂²×C₄×D₄×C₁₉	C₂	semidirect
4. C₁₉×#2535	C₂	direct (N × H)
5. C₂×C₁₉×#397	C₂	semidirect
6. C₂×C₁₉×#392	C₂	semidirect
7. C₂×C₁₉×#386	C₂	semidirect
8. C₂×C₁₉×#382	C₂	semidirect
9. C₂×C₁₉×#380	C₂	semidirect
16. C₂×C₁₉×#121	C₂²	semidirect
19. C₂×C₄×D₄×C₁₉	C₂²	semidirect
20. C₂×C₄×D₄×C₁₉	C₂²	semidirect
29. C₁₉×#397	C₂²	semidirect
30. C₁₉×#392	C₂²	semidirect
31. C₁₉×#386	C₂²	semidirect
32. C₁₉×#382	C₂²	semidirect
33. C₁₉×#380	C₂²	semidirect
46. C₂²×D₄×C₁₉	D₄	semidirect
80. C₂×C₄²×C₁₉	D₄	semidirect
110. C₂×D₄×C₁₉	C₂×D₄	semidirect
146. C₄²×C₁₉	C₂×D₄	semidirect
147. C₂×#2535	C₁₉	direct (N × H)
204. C₂²×#121	C₂×C₁₉	semidirect
205. C₂²×C₄×D₄	C₂×C₁₉	semidirect
206. C₂²×C₄×D₄	C₂×C₁₉	semidirect
207. #2535	C₂×C₁₉	direct (N × H)
208. C₂×#397	C₂×C₁₉	semidirect
209. C₂×#392	C₂×C₁₉	semidirect
210. C₂×#386	C₂×C₁₉	semidirect
211. C₂×#382	C₂×C₁₉	semidirect
212. C₂×#380	C₂×C₁₉	semidirect
249. C₂×#121	C₂²×C₁₉	semidirect
252. C₂×C₄×D₄	C₂²×C₁₉	semidirect
253. C₂×C₄×D₄	C₂²×C₁₉	semidirect
262. #397	C₂²×C₁₉	semidirect
263. #392	C₂²×C₁₉	semidirect
264. #386	C₂²×C₁₉	semidirect
265. #382	C₂²×C₁₉	semidirect
266. #380	C₂²×C₁₉	semidirect
272. C₂×C₁₉	#2535	direct (N × H)
287. C₂²×D₄	D₄×C₁₉	semidirect
321. C₂×C₄²	D₄×C₁₉	semidirect
326. C₁₉	C₂×#2535	direct (N × H)
352. C₂×D₄	C₂×D₄×C₁₉	semidirect
388. C₄²	C₂×D₄×C₁₉	semidirect
477. C₂	C₁₉×#2535	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×#121	2
C₂²×C₄×D₄×C₁₉	2
C₁₉×#2535	2
C₂×C₁₉×#397	2
C₂×C₁₉×#392	2
C₂×C₁₉×#386	2
C₂×C₁₉×#382	2
C₂×C₁₉×#380	2
C₂×#2535	19

Subgroups — C2×C19×#2535 #18040844

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2535 #18040844