Subgroups — C₂×C₁₉×#2540 #18040846

Order 4864.

4566 conjugacy classes of subgroups.

The subgroup lattice has 492 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	2	yes	maximal, complemented
3	C₂²×C₁₉×#121	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2540	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₉×#399	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₉×#392	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#390	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₉	C₂²	1	4	yes	—
14	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
15	C₂×C₁₉×#124	—	2	8	no	—
16	C₂×C₁₉×#124	C₂²	1	8	yes	complemented
17	C₂×C₁₉×C₂²⋊Q₈	—	2	16	no	—
18	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	16	yes	complemented
19	C₂×C₁₉×#121	—	2	16	no	—
20	C₂×C₁₉×#121	C₂²	1	16	yes	complemented
21	C₂×C₄×D₄×C₁₉	—	2	8	no	—
22	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	complemented
23	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
27	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
28	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
31	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
33	C₁₉×#399	C₂²	1	16	yes	complemented
34	C₁₉×#392	C₂²	1	16	yes	complemented
35	C₁₉×#390	C₂²	1	32	yes	complemented
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	complemented
37	C₂×C₁₉×#95	C₂²	1	2	yes	—
38	C₂⁵×C₁₉	C₂³	1	2	yes	—
39	C₂⁵×C₁₉	C₂³	1	2	yes	—
40	C₂²×Q₈×C₁₉	—	2	8	no	—
41	C₂²×Q₈×C₁₉	—	2	4	no	—
42	C₂²×Q₈×C₁₉	C₂³	1	4	yes	—
43	C₂²×D₄×C₁₉	—	2	8	no	—
44	C₂²×D₄×C₁₉	—	2	16	no	—
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	16	no	—
47	C₂²×D₄×C₁₉	—	2	8	no	—
48	C₂²×D₄×C₁₉	—	2	4	no	—
49	C₂²×D₄×C₁₉	—	4	8	no	—
50	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₉	C₂³	1	16	yes	—
53	C₂³×C₄×C₁₉	—	2	8	no	—
54	C₂³×C₄×C₁₉	—	2	8	no	—
55	C₂³×C₄×C₁₉	—	2	8	no	—
56	C₂³×C₄×C₁₉	C₂³	1	8	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	4	yes	—
61	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₁₉×#124	—	2	32	no	—
64	C₁₉×C₂²⋊Q₈	—	2	64	no	—
65	C₁₉×#121	—	2	64	no	—
66	C₄×D₄×C₁₉	—	2	32	no	—
67	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	16	no	—
69	C₂×C₄⋊C₄×C₁₉	D₄	1	16	yes	complemented
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	16	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
81	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
82	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
83	C₂×C₄²×C₁₉	—	4	4	no	—
84	C₂×C₄²×C₁₉	D₄	1	8	yes	complemented
85	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
87	C₁₉×#95	C₂³	1	8	yes	—
88	C₂⁴×C₁₉	—	2	4	no	—
89	C₂⁴×C₁₉	—	2	4	no	—
90	C₂⁴×C₁₉	—	2	4	no	—
91	C₂⁴×C₁₉	—	2	4	no	—
92	C₂⁴×C₁₉	—	2	4	no	—
93	C₂⁴×C₁₉	—	2	4	no	—
94	C₂⁴×C₁₉	—	2	4	no	—
95	C₂⁴×C₁₉	—	2	8	no	—
96	C₂⁴×C₁₉	—	2	8	no	—
97	C₂⁴×C₁₉	—	2	4	no	—
98	C₂⁴×C₁₉	—	2	4	no	—
99	C₂⁴×C₁₉	#41	1	8	yes	—
100	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
101	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
102	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
103	C₂×Q₈×C₁₉	—	2	16	no	—
104	C₂×Q₈×C₁₉	—	2	8	no	—
105	C₂×Q₈×C₁₉	—	4	16	no	—
106	C₂×D₄×C₁₉	—	2	32	no	—
107	C₂×D₄×C₁₉	—	2	16	no	—
108	C₂×D₄×C₁₉	—	2	32	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	32	no	—
111	C₂×D₄×C₁₉	—	2	16	no	—
112	C₂×D₄×C₁₉	—	2	8	no	—
113	C₂×D₄×C₁₉	—	4	16	no	—
114	C₂×D₄×C₁₉	—	4	64	no	—
115	C₂×D₄×C₁₉	—	4	16	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	8	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	8	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	8	no	—
125	C₂²×C₄×C₁₉	—	2	4	no	—
126	C₂²×C₄×C₁₉	—	2	16	no	—
127	C₂²×C₄×C₁₉	—	2	16	no	—
128	C₂²×C₄×C₁₉	—	2	16	no	—
129	C₂²×C₄×C₁₉	—	4	32	no	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	16	yes	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
135	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
139	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
141	C₄⋊C₄×C₁₉	—	2	8	no	—
142	C₄⋊C₄×C₁₉	—	2	32	no	—
143	C₄⋊C₄×C₁₉	C₂×D₄	1	32	yes	complemented
144	C₂²⋊C₄×C₁₉	—	2	16	no	—
145	C₂²⋊C₄×C₁₉	—	2	32	no	—
146	C₂²⋊C₄×C₁₉	—	2	32	no	—
147	C₂²⋊C₄×C₁₉	—	2	16	no	—
148	C₂²⋊C₄×C₁₉	—	2	16	no	—
149	C₄²×C₁₉	—	4	8	no	—
150	C₄²×C₁₉	C₂×D₄	1	16	yes	complemented
151	C₂×#2540	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₁₉	—	2	16	no	—
153	C₂³×C₁₉	—	2	16	no	—
154	C₂³×C₁₉	—	2	16	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	4	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	2	4	no	—
162	C₂³×C₁₉	—	2	8	no	—
163	C₂³×C₁₉	—	2	8	no	—
164	C₂³×C₁₉	—	2	4	no	—
165	C₂³×C₁₉	—	2	4	no	—
166	C₂³×C₁₉	—	4	8	no	—
167	C₂³×C₁₉	—	4	8	no	—
168	C₂³×C₁₉	—	4	8	no	—
169	C₂³×C₁₉	—	4	8	no	—
170	C₂³×C₁₉	—	4	8	no	—
171	C₂³×C₁₉	—	4	8	no	—
172	C₂³×C₁₉	—	4	8	no	—
173	C₂³×C₁₉	—	4	16	no	—
174	C₂³×C₁₉	—	4	16	no	—
175	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
176	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
177	C₂³×C₁₉	C₂×#41	1	8	yes	—
178	C₂³×C₁₉	C₂×#41	1	4	yes	—
179	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
180	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
181	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
182	Q₈×C₁₉	—	4	16	no	—
183	D₄×C₁₉	—	2	32	no	—
184	D₄×C₁₉	—	4	64	no	—
185	D₄×C₁₉	—	4	16	no	—
186	C₂×C₄×C₁₉	—	2	8	no	—
187	C₂×C₄×C₁₉	—	2	8	no	—
188	C₂×C₄×C₁₉	—	2	32	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	8	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	8	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	4	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	8	no	—
198	C₂×C₄×C₁₉	—	2	4	no	—
199	C₂×C₄×C₁₉	—	4	8	no	—
200	C₂×C₄×C₁₉	—	4	8	no	—
201	C₂×C₄×C₁₉	—	4	32	no	—
202	C₂×C₄×C₁₉	#127	1	16	yes	—
203	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
204	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₁₉	C₂²×D₄	1	16	yes	—
206	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₁₉	C₂²×D₄	1	8	yes	—
208	C₂²×#124	C₂×C₁₉	1	1	yes	characteristic, complemented
209	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	2	yes	complemented
210	C₂²×#121	C₂×C₁₉	1	2	yes	complemented
211	C₂²×C₄×D₄	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#2540	C₂×C₁₉	1	16	yes	direct product factor
213	C₂×#399	C₂×C₁₉	1	2	yes	complemented
214	C₂×#392	C₂×C₁₉	1	2	yes	complemented
215	C₂×#390	C₂×C₁₉	1	4	yes	complemented
216	C₂×C₄×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic, complemented
217	C₂²×C₁₉	—	2	8	no	—
218	C₂²×C₁₉	—	2	8	no	—
219	C₂²×C₁₉	—	2	8	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	32	no	—
225	C₂²×C₁₉	—	4	4	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	4	8	no	—
229	C₂²×C₁₉	—	4	8	no	—
230	C₂²×C₁₉	—	8	16	no	—
231	C₂²×C₁₉	#525	1	4	yes	—
232	C₂²×C₁₉	C₂×#127	1	4	yes	—
233	C₂²×C₁₉	#537	1	4	yes	—
234	C₂²×C₁₉	#546	1	8	yes	—
235	C₂²×C₁₉	#548	1	8	yes	—
236	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
237	C₂²×C₁₉	C₂³×D₄	1	2	yes	—
238	C₂²×C₁₉	C₂²×#41	1	2	yes	—
239	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
241	C₄×C₁₉	—	2	4	no	—
242	C₄×C₁₉	—	2	4	no	—
243	C₄×C₁₉	—	2	16	no	—
244	C₄×C₁₉	—	4	4	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	C₂×#127	1	8	yes	—
247	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
249	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
250	C₂³×D₄	C₂²×C₁₉	1	4	yes	—
251	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
252	C₂×#124	—	2	8	no	—
253	C₂×#124	C₂²×C₁₉	1	8	yes	complemented
254	C₂×C₂²⋊Q₈	—	2	16	no	—
255	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	16	yes	complemented
256	C₂×#121	—	2	16	no	—
257	C₂×#121	C₂²×C₁₉	1	16	yes	complemented
258	C₂×C₄×D₄	—	2	8	no	—
259	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	complemented
260	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
262	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
263	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
264	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
265	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
266	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
268	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
269	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
270	#399	C₂²×C₁₉	1	16	yes	complemented
271	#392	C₂²×C₁₉	1	16	yes	complemented
272	#390	C₂²×C₁₉	1	32	yes	complemented
273	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	complemented
274	C₂×#95	C₂²×C₁₉	1	2	yes	—
275	C₂×C₁₉	—	4	8	no	—
276	C₂×C₁₉	—	8	4	no	—
277	C₂×C₁₉	#2540	1	8	yes	direct product factor
278	C₂×C₁₉	C₂×#525	1	1	yes	characteristic
279	C₂×C₁₉	C₂²×#127	1	1	yes	characteristic
280	C₂×C₁₉	C₂×#537	1	1	yes	characteristic
281	C₂×C₁₉	C₂×#546	1	2	yes	—
282	C₂×C₁₉	C₂×#548	1	2	yes	—
283	C₂⁵	C₂³×C₁₉	1	2	yes	—
284	C₂⁵	C₂³×C₁₉	1	2	yes	—
285	C₂²×Q₈	—	2	8	no	—
286	C₂²×Q₈	—	2	4	no	—
287	C₂²×Q₈	C₂³×C₁₉	1	4	yes	—
288	C₂²×D₄	—	2	8	no	—
289	C₂²×D₄	—	2	16	no	—
290	C₂²×D₄	—	2	4	no	—
291	C₂²×D₄	—	2	16	no	—
292	C₂²×D₄	—	2	8	no	—
293	C₂²×D₄	—	2	4	no	—
294	C₂²×D₄	—	4	8	no	—
295	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
296	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
297	C₂²×D₄	C₂³×C₁₉	1	16	yes	—
298	C₂³×C₄	—	2	8	no	—
299	C₂³×C₄	—	2	8	no	—
300	C₂³×C₄	—	2	8	no	—
301	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
302	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
303	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
304	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
306	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
308	#124	—	2	32	no	—
309	C₂²⋊Q₈	—	2	64	no	—
310	#121	—	2	64	no	—
311	C₄×D₄	—	2	32	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	—	2	16	no	—
314	C₂×C₄⋊C₄	D₄×C₁₉	1	16	yes	complemented
315	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
318	C₂×C₂²⋊C₄	—	2	8	no	—
319	C₂×C₂²⋊C₄	—	2	16	no	—
320	C₂×C₂²⋊C₄	—	2	16	no	—
321	C₂×C₂²⋊C₄	—	2	8	no	—
322	C₂×C₂²⋊C₄	—	2	8	no	—
323	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
326	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
327	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
328	C₂×C₄²	—	4	4	no	—
329	C₂×C₄²	D₄×C₁₉	1	8	yes	complemented
330	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
331	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
332	#95	C₂³×C₁₉	1	8	yes	—
333	C₁₉	C₂×#2540	1	1	yes	characteristic, direct product factor, Sylow
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	2	4	no	—
337	C₂⁴	—	2	4	no	—
338	C₂⁴	—	2	4	no	—
339	C₂⁴	—	2	4	no	—
340	C₂⁴	—	2	4	no	—
341	C₂⁴	—	2	8	no	—
342	C₂⁴	—	2	8	no	—
343	C₂⁴	—	2	4	no	—
344	C₂⁴	—	2	4	no	—
345	C₂⁴	#41×C₁₉	1	8	yes	—
346	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
347	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
348	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
349	C₂×Q₈	—	2	16	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	4	16	no	—
352	C₂×D₄	—	2	32	no	—
353	C₂×D₄	—	2	16	no	—
354	C₂×D₄	—	2	32	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	32	no	—
357	C₂×D₄	—	2	16	no	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	4	16	no	—
360	C₂×D₄	—	4	64	no	—
361	C₂×D₄	—	4	16	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	8	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	16	no	—
373	C₂²×C₄	—	2	16	no	—
374	C₂²×C₄	—	2	16	no	—
375	C₂²×C₄	—	4	32	no	—
376	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
377	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
378	C₂²×C₄	C₂×D₄×C₁₉	1	16	yes	—
379	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
381	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
383	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
385	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	32	no	—
389	C₄⋊C₄	C₂×D₄×C₁₉	1	32	yes	complemented
390	C₂²⋊C₄	—	2	16	no	—
391	C₂²⋊C₄	—	2	32	no	—
392	C₂²⋊C₄	—	2	32	no	—
393	C₂²⋊C₄	—	2	16	no	—
394	C₂²⋊C₄	—	2	16	no	—
395	C₄²	—	4	8	no	—
396	C₄²	C₂×D₄×C₁₉	1	16	yes	complemented
397	C₂³	—	2	16	no	—
398	C₂³	—	2	16	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	2	4	no	—
407	C₂³	—	2	8	no	—
408	C₂³	—	2	8	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	4	8	no	—
412	C₂³	—	4	8	no	—
413	C₂³	—	4	8	no	—
414	C₂³	—	4	8	no	—
415	C₂³	—	4	8	no	—
416	C₂³	—	4	8	no	—
417	C₂³	—	4	8	no	—
418	C₂³	—	4	16	no	—
419	C₂³	—	4	16	no	—
420	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
421	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
422	C₂³	C₂×#41×C₁₉	1	8	yes	—
423	C₂³	C₂×#41×C₁₉	1	4	yes	—
424	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
425	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
426	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
427	Q₈	—	4	16	no	—
428	D₄	—	2	32	no	—
429	D₄	—	4	64	no	—
430	D₄	—	4	16	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	32	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	8	no	—
446	C₂×C₄	—	4	32	no	—
447	C₂×C₄	C₁₉×#127	1	16	yes	—
448	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
449	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
450	C₂×C₄	C₂²×D₄×C₁₉	1	16	yes	—
451	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
452	C₂×C₄	C₂²×D₄×C₁₉	1	8	yes	—
453	C₂²	—	2	8	no	—
454	C₂²	—	2	8	no	—
455	C₂²	—	2	8	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	32	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	8	no	—
465	C₂²	—	4	8	no	—
466	C₂²	—	8	16	no	—
467	C₂²	C₁₉×#525	1	4	yes	—
468	C₂²	C₂×C₁₉×#127	1	4	yes	—
469	C₂²	C₁₉×#537	1	4	yes	—
470	C₂²	C₁₉×#546	1	8	yes	—
471	C₂²	C₁₉×#548	1	8	yes	—
472	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
473	C₂²	C₂³×D₄×C₁₉	1	2	yes	—
474	C₂²	C₂²×#41×C₁₉	1	2	yes	—
475	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
477	C₄	—	2	4	no	—
478	C₄	—	2	4	no	—
479	C₄	—	2	16	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	4	no	—
482	C₄	C₂×C₁₉×#127	1	8	yes	—
483	C₂	—	4	8	no	—
484	C₂	—	8	4	no	—
485	C₂	C₁₉×#2540	1	8	yes	direct product factor
486	C₂	C₂×C₁₉×#525	1	1	yes	characteristic
487	C₂	C₂²×C₁₉×#127	1	1	yes	characteristic
488	C₂	C₂×C₁₉×#537	1	1	yes	characteristic
489	C₂	C₂×C₁₉×#546	1	2	yes	—
490	C₂	C₂×C₁₉×#548	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×#124	C₂	semidirect
2. C₂²×C₁₉×C₂²⋊Q₈	C₂	semidirect
3. C₂²×C₁₉×#121	C₂	semidirect
4. C₂²×C₄×D₄×C₁₉	C₂	semidirect
5. C₁₉×#2540	C₂	direct (N × H)
6. C₂×C₁₉×#399	C₂	semidirect
7. C₂×C₁₉×#392	C₂	semidirect
8. C₂×C₁₉×#390	C₂	semidirect
9. C₂×C₄×C₄⋊C₄×C₁₉	C₂	semidirect
16. C₂×C₁₉×#124	C₂²	semidirect
18. C₂×C₁₉×C₂²⋊Q₈	C₂²	semidirect
20. C₂×C₁₉×#121	C₂²	semidirect
22. C₂×C₄×D₄×C₁₉	C₂²	semidirect
33. C₁₉×#399	C₂²	semidirect
34. C₁₉×#392	C₂²	semidirect
35. C₁₉×#390	C₂²	semidirect
36. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
69. C₂×C₄⋊C₄×C₁₉	D₄	semidirect
84. C₂×C₄²×C₁₉	D₄	semidirect
143. C₄⋊C₄×C₁₉	C₂×D₄	semidirect
150. C₄²×C₁₉	C₂×D₄	semidirect
151. C₂×#2540	C₁₉	direct (N × H)
208. C₂²×#124	C₂×C₁₉	semidirect
209. C₂²×C₂²⋊Q₈	C₂×C₁₉	semidirect
210. C₂²×#121	C₂×C₁₉	semidirect
211. C₂²×C₄×D₄	C₂×C₁₉	semidirect
212. #2540	C₂×C₁₉	direct (N × H)
213. C₂×#399	C₂×C₁₉	semidirect
214. C₂×#392	C₂×C₁₉	semidirect
215. C₂×#390	C₂×C₁₉	semidirect
216. C₂×C₄×C₄⋊C₄	C₂×C₁₉	semidirect
253. C₂×#124	C₂²×C₁₉	semidirect
255. C₂×C₂²⋊Q₈	C₂²×C₁₉	semidirect
257. C₂×#121	C₂²×C₁₉	semidirect
259. C₂×C₄×D₄	C₂²×C₁₉	semidirect
270. #399	C₂²×C₁₉	semidirect
271. #392	C₂²×C₁₉	semidirect
272. #390	C₂²×C₁₉	semidirect
273. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
277. C₂×C₁₉	#2540	direct (N × H)
314. C₂×C₄⋊C₄	D₄×C₁₉	semidirect
329. C₂×C₄²	D₄×C₁₉	semidirect
333. C₁₉	C₂×#2540	direct (N × H)
389. C₄⋊C₄	C₂×D₄×C₁₉	semidirect
396. C₄²	C₂×D₄×C₁₉	semidirect
485. C₂	C₁₉×#2540	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×#2540	2
C₂×C₁₉×#399	2
C₂×C₁₉×#392	2
C₂×C₁₉×#390	2
C₂×C₄×C₄⋊C₄×C₁₉	2
C₂×#2540	19

Subgroups — C2×C19×#2540 #18040846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2540 #18040846