Subgroups — C₂×C₁₉×#2624 #18040567

Order 4864.

3110 conjugacy classes of subgroups.

The subgroup lattice has 440 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	1	yes	maximal, characteristic
2	C₂²×C₁₉×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2624	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₉×#399	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#394	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₉×#390	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₉×#389	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#121	—	2	8	no	—
14	C₂×C₁₉×#121	C₂²	1	8	yes	—
15	C₂×C₁₉×#117	—	2	8	no	—
16	C₂×C₁₉×#117	C₂²	1	8	yes	complemented
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
22	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
26	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
27	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
28	C₁₉×#399	C₂²	1	16	yes	complemented
29	C₁₉×#397	C₂²	1	16	yes	complemented
30	C₁₉×#394	C₂²	1	32	yes	complemented
31	C₁₉×#390	C₂²	1	16	yes	complemented
32	C₁₉×#389	C₂²	1	16	yes	complemented
33	C₁₉×#380	C₂²	1	8	yes	complemented
34	C₂×C₁₉×#95	C₂²	1	2	yes	—
35	C₂×C₁₉×#95	C₂²	1	4	yes	—
36	C₂⁵×C₁₉	C₂³	1	2	yes	—
37	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
38	C₂²×D₄×C₁₉	—	2	8	no	—
39	C₂²×D₄×C₁₉	—	2	4	no	—
40	C₂²×D₄×C₁₉	—	2	8	no	—
41	C₂²×D₄×C₁₉	—	4	8	no	—
42	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
43	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
44	C₂³×C₄×C₁₉	—	2	8	no	—
45	C₂³×C₄×C₁₉	D₄	1	8	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₁₉×#121	—	2	32	no	—
54	C₁₉×#117	—	2	32	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
59	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	16	yes	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₁₉	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	4	8	no	—
70	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
71	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
74	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
75	C₂×C₄²×C₁₉	—	2	8	no	—
76	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
77	C₁₉×#95	C₂³	1	8	yes	—
78	C₁₉×#95	C₂³	1	16	yes	—
79	C₂⁴×C₁₉	—	2	4	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	4	no	—
82	C₂⁴×C₁₉	—	2	2	no	—
83	C₂⁴×C₁₉	—	2	4	no	—
84	C₂⁴×C₁₉	—	2	8	no	—
85	C₂⁴×C₁₉	—	2	4	no	—
86	C₂⁴×C₁₉	—	2	8	no	—
87	C₂⁴×C₁₉	—	2	4	no	—
88	C₂⁴×C₁₉	C₂×D₄	1	4	yes	—
89	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
90	C₂⁴×C₁₉	C₂⁴	1	2	yes	—
91	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
92	C₂×D₄×C₁₉	—	2	16	no	—
93	C₂×D₄×C₁₉	—	2	8	no	—
94	C₂×D₄×C₁₉	—	2	16	no	—
95	C₂×D₄×C₁₉	—	4	16	no	—
96	C₂×D₄×C₁₉	—	4	32	no	—
97	C₂×D₄×C₁₉	—	4	16	no	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	32	no	—
100	C₂²×C₄×C₁₉	—	2	16	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	8	no	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	8	no	—
108	C₂²×C₄×C₁₉	—	2	8	no	—
109	C₂²×C₄×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	8	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	16	yes	—
114	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₉	#41	1	8	yes	—
116	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
122	C₄⋊C₄×C₁₉	—	2	8	no	—
123	C₄⋊C₄×C₁₉	—	2	8	no	—
124	C₄⋊C₄×C₁₉	—	2	8	no	—
125	C₄⋊C₄×C₁₉	—	2	16	no	—
126	C₄⋊C₄×C₁₉	—	4	16	no	—
127	C₂²⋊C₄×C₁₉	—	2	16	no	—
128	C₂²⋊C₄×C₁₉	—	2	16	no	—
129	C₂²⋊C₄×C₁₉	—	4	8	no	—
130	C₂²⋊C₄×C₁₉	—	4	16	no	—
131	C₂²⋊C₄×C₁₉	—	4	16	no	—
132	C₄²×C₁₉	—	2	16	no	—
133	C₂×#2624	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₁₉	—	2	8	no	—
135	C₂³×C₁₉	—	2	8	no	—
136	C₂³×C₁₉	—	2	8	no	—
137	C₂³×C₁₉	—	2	4	no	—
138	C₂³×C₁₉	—	2	2	no	—
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	4	no	—
142	C₂³×C₁₉	—	2	8	no	—
143	C₂³×C₁₉	—	2	4	no	—
144	C₂³×C₁₉	—	2	8	no	—
145	C₂³×C₁₉	—	2	4	no	—
146	C₂³×C₁₉	—	4	8	no	—
147	C₂³×C₁₉	—	4	8	no	—
148	C₂³×C₁₉	—	4	8	no	—
149	C₂³×C₁₉	—	4	8	no	—
150	C₂³×C₁₉	—	4	8	no	—
151	C₂³×C₁₉	—	4	16	no	—
152	C₂³×C₁₉	—	4	16	no	—
153	C₂³×C₁₉	C₂²×D₄	1	4	yes	—
154	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
155	C₂³×C₁₉	C₂×#41	1	4	yes	—
156	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
157	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
158	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
159	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
160	D₄×C₁₉	—	4	32	no	—
161	D₄×C₁₉	—	4	16	no	—
162	C₂×C₄×C₁₉	—	2	8	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	32	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	8	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	8	no	—
172	C₂×C₄×C₁₉	—	2	8	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	8	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	4	8	no	—
177	C₂×C₄×C₁₉	—	4	8	no	—
178	C₂×C₄×C₁₉	—	4	8	no	—
179	C₂×C₄×C₁₉	—	4	16	no	—
180	C₂×C₄×C₁₉	#123	1	16	yes	—
181	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
183	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
184	C₂²×#121	C₂×C₁₉	1	1	yes	characteristic
185	C₂²×#117	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#2624	C₂×C₁₉	1	16	yes	direct product factor
187	C₂×#399	C₂×C₁₉	1	2	yes	complemented
188	C₂×#397	C₂×C₁₉	1	2	yes	complemented
189	C₂×#394	C₂×C₁₉	1	4	yes	complemented
190	C₂×#390	C₂×C₁₉	1	2	yes	complemented
191	C₂×#389	C₂×C₁₉	1	2	yes	complemented
192	C₂×#380	C₂×C₁₉	1	1	yes	characteristic, complemented
193	C₂²×C₁₉	—	2	4	no	—
194	C₂²×C₁₉	—	2	4	no	—
195	C₂²×C₁₉	—	2	4	no	—
196	C₂²×C₁₉	—	4	16	no	—
197	C₂²×C₁₉	—	4	4	no	—
198	C₂²×C₁₉	—	4	4	no	—
199	C₂²×C₁₉	—	4	4	no	—
200	C₂²×C₁₉	—	4	4	no	—
201	C₂²×C₁₉	—	4	4	no	—
202	C₂²×C₁₉	—	4	8	no	—
203	C₂²×C₁₉	—	4	8	no	—
204	C₂²×C₁₉	—	8	16	no	—
205	C₂²×C₁₉	C₂×#123	1	4	yes	—
206	C₂²×C₁₉	#535	1	4	yes	—
207	C₂²×C₁₉	#537	1	4	yes	—
208	C₂²×C₁₉	#540	1	8	yes	—
209	C₂²×C₁₉	#542	1	8	yes	—
210	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
211	C₂²×C₁₉	C₂²×#41	1	2	yes	—
212	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
213	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
214	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
215	C₄×C₁₉	—	2	4	no	—
216	C₄×C₁₉	—	4	4	no	—
217	C₄×C₁₉	—	4	4	no	—
218	C₄×C₁₉	—	4	4	no	—
219	C₄×C₁₉	—	4	8	no	—
220	C₄×C₁₉	C₂×#123	1	8	yes	—
221	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
222	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
223	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
224	C₂×#121	—	2	8	no	—
225	C₂×#121	C₂²×C₁₉	1	8	yes	—
226	C₂×#117	—	2	8	no	—
227	C₂×#117	C₂²×C₁₉	1	8	yes	complemented
228	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
233	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
238	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
239	#399	C₂²×C₁₉	1	16	yes	complemented
240	#397	C₂²×C₁₉	1	16	yes	complemented
241	#394	C₂²×C₁₉	1	32	yes	complemented
242	#390	C₂²×C₁₉	1	16	yes	complemented
243	#389	C₂²×C₁₉	1	16	yes	complemented
244	#380	C₂²×C₁₉	1	8	yes	complemented
245	C₂×#95	C₂²×C₁₉	1	4	yes	—
246	C₂×#95	C₂²×C₁₉	1	2	yes	—
247	C₂×C₁₉	—	4	4	no	—
248	C₂×C₁₉	—	8	4	no	—
249	C₂×C₁₉	#2624	1	8	yes	direct product factor
250	C₂×C₁₉	C₂²×#123	1	1	yes	characteristic
251	C₂×C₁₉	C₂×#535	1	1	yes	characteristic
252	C₂×C₁₉	C₂×#537	1	1	yes	characteristic
253	C₂×C₁₉	C₂×#540	1	2	yes	—
254	C₂×C₁₉	C₂×#542	1	2	yes	—
255	C₂⁵	C₂³×C₁₉	1	2	yes	—
256	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
257	C₂²×D₄	—	2	8	no	—
258	C₂²×D₄	—	2	4	no	—
259	C₂²×D₄	—	2	8	no	—
260	C₂²×D₄	—	4	8	no	—
261	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
262	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
263	C₂³×C₄	—	2	8	no	—
264	C₂³×C₄	D₄×C₁₉	1	8	yes	—
265	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
266	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
267	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
268	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
269	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
271	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
272	#121	—	2	32	no	—
273	#117	—	2	32	no	—
274	C₂×C₄⋊C₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	4	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	8	no	—
278	C₂×C₄⋊C₄	—	4	8	no	—
279	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
281	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₉	1	16	yes	—
284	C₂×C₂²⋊C₄	—	2	8	no	—
285	C₂×C₂²⋊C₄	—	2	8	no	—
286	C₂×C₂²⋊C₄	—	4	4	no	—
287	C₂×C₂²⋊C₄	—	4	8	no	—
288	C₂×C₂²⋊C₄	—	4	8	no	—
289	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
294	C₂×C₄²	—	2	8	no	—
295	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
296	#95	C₂³×C₁₉	1	8	yes	—
297	#95	C₂³×C₁₉	1	16	yes	—
298	C₁₉	C₂×#2624	1	1	yes	characteristic, direct product factor, Sylow
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	2	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	8	no	—
305	C₂⁴	—	2	4	no	—
306	C₂⁴	—	2	8	no	—
307	C₂⁴	—	2	4	no	—
308	C₂⁴	C₂×D₄×C₁₉	1	4	yes	—
309	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
310	C₂⁴	C₂⁴×C₁₉	1	2	yes	—
311	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
312	C₂×D₄	—	2	16	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	16	no	—
315	C₂×D₄	—	4	16	no	—
316	C₂×D₄	—	4	32	no	—
317	C₂×D₄	—	4	16	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	32	no	—
320	C₂²×C₄	—	2	16	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	16	yes	—
334	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
335	C₂²×C₄	#41×C₁₉	1	8	yes	—
336	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
338	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
339	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	16	no	—
346	C₄⋊C₄	—	4	16	no	—
347	C₂²⋊C₄	—	2	16	no	—
348	C₂²⋊C₄	—	2	16	no	—
349	C₂²⋊C₄	—	4	8	no	—
350	C₂²⋊C₄	—	4	16	no	—
351	C₂²⋊C₄	—	4	16	no	—
352	C₄²	—	2	16	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	4	8	no	—
366	C₂³	—	4	8	no	—
367	C₂³	—	4	8	no	—
368	C₂³	—	4	8	no	—
369	C₂³	—	4	8	no	—
370	C₂³	—	4	16	no	—
371	C₂³	—	4	16	no	—
372	C₂³	C₂²×D₄×C₁₉	1	4	yes	—
373	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
374	C₂³	C₂×#41×C₁₉	1	4	yes	—
375	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
376	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
377	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
378	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
379	D₄	—	4	32	no	—
380	D₄	—	4	16	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	32	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	16	no	—
399	C₂×C₄	C₁₉×#123	1	16	yes	—
400	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
401	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
402	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	16	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	4	no	—
412	C₂²	—	4	8	no	—
413	C₂²	—	4	8	no	—
414	C₂²	—	8	16	no	—
415	C₂²	C₂×C₁₉×#123	1	4	yes	—
416	C₂²	C₁₉×#535	1	4	yes	—
417	C₂²	C₁₉×#537	1	4	yes	—
418	C₂²	C₁₉×#540	1	8	yes	—
419	C₂²	C₁₉×#542	1	8	yes	—
420	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
421	C₂²	C₂²×#41×C₁₉	1	2	yes	—
422	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
423	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
425	C₄	—	2	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	8	no	—
430	C₄	C₂×C₁₉×#123	1	8	yes	—
431	C₂	—	4	4	no	—
432	C₂	—	8	4	no	—
433	C₂	C₁₉×#2624	1	8	yes	direct product factor
434	C₂	C₂²×C₁₉×#123	1	1	yes	characteristic
435	C₂	C₂×C₁₉×#535	1	1	yes	characteristic
436	C₂	C₂×C₁₉×#537	1	1	yes	characteristic
437	C₂	C₂×C₁₉×#540	1	2	yes	—
438	C₂	C₂×C₁₉×#542	1	2	yes	—

	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
2. C₂²×C₁₉×#117	C₂	semidirect
3. C₁₉×#2624	C₂	direct (N × H)
4. C₂×C₁₉×#399	C₂	semidirect
5. C₂×C₁₉×#397	C₂	semidirect
6. C₂×C₁₉×#394	C₂	semidirect
7. C₂×C₁₉×#390	C₂	semidirect
8. C₂×C₁₉×#389	C₂	semidirect
9. C₂×C₁₉×#380	C₂	semidirect
16. C₂×C₁₉×#117	C₂²	semidirect
28. C₁₉×#399	C₂²	semidirect
29. C₁₉×#397	C₂²	semidirect
30. C₁₉×#394	C₂²	semidirect
31. C₁₉×#390	C₂²	semidirect
32. C₁₉×#389	C₂²	semidirect
33. C₁₉×#380	C₂²	semidirect
133. C₂×#2624	C₁₉	direct (N × H)
185. C₂²×#117	C₂×C₁₉	semidirect
186. #2624	C₂×C₁₉	direct (N × H)
187. C₂×#399	C₂×C₁₉	semidirect
188. C₂×#397	C₂×C₁₉	semidirect
189. C₂×#394	C₂×C₁₉	semidirect
190. C₂×#390	C₂×C₁₉	semidirect
191. C₂×#389	C₂×C₁₉	semidirect
192. C₂×#380	C₂×C₁₉	semidirect
227. C₂×#117	C₂²×C₁₉	semidirect
239. #399	C₂²×C₁₉	semidirect
240. #397	C₂²×C₁₉	semidirect
241. #394	C₂²×C₁₉	semidirect
242. #390	C₂²×C₁₉	semidirect
243. #389	C₂²×C₁₉	semidirect
244. #380	C₂²×C₁₉	semidirect
249. C₂×C₁₉	#2624	direct (N × H)
298. C₁₉	C₂×#2624	direct (N × H)
433. C₂	C₁₉×#2624	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×C₁₉×#117	2
C₁₉×#2624	2
C₂×C₁₉×#399	2
C₂×C₁₉×#397	2
C₂×C₁₉×#394	2
C₂×C₁₉×#390	2
C₂×C₁₉×#389	2
C₂×C₁₉×#380	2
C₂×#2624	19

Subgroups — C2×C19×#2624 #18040567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#2624 #18040567