Subgroups — C₂×C₁₉×#1598 #18024067

Order 4864.

1652 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#447	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1598	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₉×#327	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#324	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₁₉	—	2	1	no	—
8	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×D₈×C₁₉	—	2	2	no	—
10	C₁₉×#537	—	2	4	no	—
11	C₁₉×#537	—	2	2	no	—
12	C₁₉×#537	C₂²	1	4	yes	complemented
13	C₂×C₁₉×C₂²⋊Q₈	—	2	2	no	—
14	C₂×C₁₉×#121	—	2	2	no	—
15	C₂×C₁₉×#121	—	2	1	no	—
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
19	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
20	C₁₉×#447	—	2	4	no	—
21	C₁₉×#447	C₂²	1	8	yes	complemented
22	C₂×C₁₉×#102	—	2	2	no	—
23	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₁₉×#394	—	2	2	no	—
25	C₁₉×#394	C₂²	1	4	yes	complemented
26	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
27	C₁₉×#327	C₂²	1	8	yes	complemented
28	C₁₉×#324	C₂²	1	4	yes	complemented
29	C₂⁵×C₁₉	—	2	1	no	—
30	C₂×#41×C₁₉	—	2	4	no	—
31	C₂×#41×C₁₉	—	2	4	no	—
32	C₂×#41×C₁₉	—	4	4	no	—
33	C₂×#41×C₁₉	—	4	4	no	—
34	C₂²×Q₈×C₁₉	—	2	1	no	—
35	C₂²×D₄×C₁₉	—	2	1	no	—
36	C₂²×D₄×C₁₉	—	2	2	no	—
37	C₂²×D₄×C₁₉	—	2	1	no	—
38	C₂²×D₄×C₁₉	—	2	2	no	—
39	C₂²×D₄×C₁₉	—	2	2	no	—
40	C₂²×D₄×C₁₉	—	2	1	no	—
41	C₂²×D₄×C₁₉	—	4	4	no	—
42	C₂²×D₄×C₁₉	D₄	1	2	yes	—
43	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	—	2	2	no	—
45	C₂³×C₄×C₁₉	—	2	1	no	—
46	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₁₉	—	2	8	no	—
50	C₂×D₈×C₁₉	—	4	8	no	—
51	C₂²×C₈×C₁₉	—	2	2	no	—
52	C₁₉×C₂²⋊Q₈	—	2	8	no	—
53	C₁₉×C₂²⋊Q₈	—	2	8	no	—
54	C₁₉×#121	—	2	4	no	—
55	C₁₉×#121	—	2	8	no	—
56	C₁₉×#121	—	2	8	no	—
57	C₁₉×#121	—	2	4	no	—
58	C₁₉×#121	—	2	2	no	—
59	C₁₉×#121	—	2	2	no	—
60	C₁₉×#121	D₄	1	4	yes	—
61	C₁₉×#121	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
74	C₁₉×#102	—	2	8	no	—
75	C₁₉×C₂²⋊C₈	—	2	2	no	—
76	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
77	C₁₉×#95	—	2	1	no	—
78	C₁₉×#95	C₂³	1	2	yes	—
79	C₂⁴×C₁₉	—	2	4	no	—
80	C₂⁴×C₁₉	—	2	2	no	—
81	C₂⁴×C₁₉	—	2	2	no	—
82	C₂⁴×C₁₉	—	4	2	no	—
83	C₂⁴×C₁₉	—	4	2	no	—
84	C₂⁴×C₁₉	—	4	2	no	—
85	C₂⁴×C₁₉	—	4	1	no	—
86	C₂⁴×C₁₉	—	4	1	no	—
87	C₂⁴×C₁₉	—	4	2	no	—
88	C₂⁴×C₁₉	—	4	2	no	—
89	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
90	#41×C₁₉	—	4	8	no	—
91	#41×C₁₉	—	4	16	no	—
92	#41×C₁₉	—	4	8	no	—
93	C₂×Q₈×C₁₉	—	2	4	no	—
94	C₂×Q₈×C₁₉	—	4	4	no	—
95	C₂×D₄×C₁₉	—	2	8	no	—
96	C₂×D₄×C₁₉	—	2	4	no	—
97	C₂×D₄×C₁₉	—	2	4	no	—
98	C₂×D₄×C₁₉	—	2	4	no	—
99	C₂×D₄×C₁₉	—	2	4	no	—
100	C₂×D₄×C₁₉	—	2	2	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	4	4	no	—
103	C₂×D₄×C₁₉	—	4	4	no	—
104	C₂×D₄×C₁₉	—	4	4	no	—
105	C₂×D₄×C₁₉	—	4	4	no	—
106	C₂×D₄×C₁₉	—	4	8	no	—
107	C₂×D₄×C₁₉	—	4	4	no	—
108	C₂×D₄×C₁₉	—	4	4	no	—
109	C₂×D₄×C₁₉	—	4	4	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	8	2	no	—
112	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	1	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	8	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	4	2	no	—
122	C₂²×C₄×C₁₉	—	4	8	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	—	4	2	no	—
125	C₂²×C₄×C₁₉	—	4	2	no	—
126	C₂²×C₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	D₈	1	4	yes	complemented
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
134	D₈×C₁₉	—	4	16	no	—
135	C₂×C₈×C₁₉	—	2	4	no	—
136	C₂×C₈×C₁₉	—	4	4	no	—
137	C₄⋊C₄×C₁₉	—	2	4	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
142	C₂²⋊C₄×C₁₉	—	2	8	no	—
143	C₂²⋊C₄×C₁₉	—	2	4	no	—
144	C₂²⋊C₄×C₁₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₉	—	4	8	no	—
146	C₂²⋊C₄×C₁₉	—	4	8	no	—
147	C₂×#1598	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	2	2	no	—
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	2	4	no	—
151	C₂³×C₁₉	—	2	4	no	—
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	—	4	4	no	—
154	C₂³×C₁₉	—	4	8	no	—
155	C₂³×C₁₉	—	4	8	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	4	no	—
162	C₂³×C₁₉	—	4	4	no	—
163	C₂³×C₁₉	—	4	4	no	—
164	C₂³×C₁₉	—	4	4	no	—
165	C₂³×C₁₉	—	8	4	no	—
166	C₂³×C₁₉	—	8	4	no	—
167	C₂³×C₁₉	—	8	2	no	—
168	C₂³×C₁₉	—	8	2	no	—
169	C₂³×C₁₉	—	8	2	no	—
170	C₂³×C₁₉	—	8	2	no	—
171	C₂³×C₁₉	#120	1	1	yes	characteristic
172	C₂³×C₁₉	#120	1	1	yes	characteristic
173	C₂³×C₁₉	C₂×D₈	1	2	yes	—
174	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
175	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₁₉	—	4	8	no	—
177	D₄×C₁₉	—	2	8	no	—
178	D₄×C₁₉	—	4	4	no	—
179	D₄×C₁₉	—	4	4	no	—
180	D₄×C₁₉	—	4	8	no	—
181	D₄×C₁₉	—	4	8	no	—
182	D₄×C₁₉	—	4	4	no	—
183	D₄×C₁₉	—	4	4	no	—
184	D₄×C₁₉	—	4	8	no	—
185	D₄×C₁₉	—	8	2	no	—
186	D₄×C₁₉	—	8	4	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	4	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	2	4	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	16	no	—
198	C₂×C₄×C₁₉	—	4	4	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	8	1	no	—
205	C₂×C₄×C₁₉	—	8	4	no	—
206	C₂×C₄×C₁₉	#120	1	2	yes	—
207	C₂×C₄×C₁₉	C₂×D₈	1	4	yes	complemented
208	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
209	C₈×C₁₉	—	4	4	no	—
210	C₂×#537	C₂×C₁₉	1	1	yes	characteristic, complemented
211	C₂×#447	C₂×C₁₉	1	2	yes	complemented
212	C₂×#394	C₂×C₁₉	1	1	yes	characteristic, complemented
213	#1598	C₂×C₁₉	1	8	yes	direct product factor
214	C₂×#327	C₂×C₁₉	1	2	yes	complemented
215	C₂×#324	C₂×C₁₉	1	1	yes	characteristic, complemented
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	2	4	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	1	no	—
221	C₂²×C₁₉	—	2	1	no	—
222	C₂²×C₁₉	—	4	4	no	—
223	C₂²×C₁₉	—	4	4	no	—
224	C₂²×C₁₉	—	4	4	no	—
225	C₂²×C₁₉	—	4	4	no	—
226	C₂²×C₁₉	—	4	4	no	—
227	C₂²×C₁₉	—	4	4	no	—
228	C₂²×C₁₉	—	8	2	no	—
229	C₂²×C₁₉	—	8	2	no	—
230	C₂²×C₁₉	—	8	8	no	—
231	C₂²×C₁₉	—	8	8	no	—
232	C₂²×C₁₉	—	8	8	no	—
233	C₂²×C₁₉	—	8	2	no	—
234	C₂²×C₁₉	—	8	2	no	—
235	C₂²×C₁₉	#447	1	2	yes	—
236	C₂²×C₁₉	#447	1	2	yes	—
237	C₂²×C₁₉	#454	1	2	yes	—
238	C₂²×C₁₉	B(4,𝔽₂)	1	2	yes	—
239	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
240	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
241	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₄×C₁₉	—	2	4	no	—
243	C₄×C₁₉	—	2	2	no	—
244	C₄×C₁₉	—	2	2	no	—
245	C₄×C₁₉	—	4	4	no	—
246	C₄×C₁₉	—	4	2	no	—
247	C₄×C₁₉	—	8	2	no	—
248	C₂²×#41	—	2	1	no	—
249	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
250	C₂²×D₈	—	2	2	no	—
251	#537	—	2	4	no	—
252	#537	—	2	2	no	—
253	#537	C₂²×C₁₉	1	4	yes	complemented
254	C₂×C₂²⋊Q₈	—	2	2	no	—
255	C₂×#121	—	2	2	no	—
256	C₂×#121	—	2	1	no	—
257	C₂×#121	C₂²×C₁₉	1	2	yes	—
258	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	—	2	1	no	—
260	C₂²×C₂²⋊C₄	—	2	1	no	—
261	#447	—	2	4	no	—
262	#447	C₂²×C₁₉	1	8	yes	complemented
263	C₂×#102	—	2	2	no	—
264	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
265	#394	—	2	2	no	—
266	#394	C₂²×C₁₉	1	4	yes	complemented
267	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
268	#327	C₂²×C₁₉	1	8	yes	complemented
269	#324	C₂²×C₁₉	1	4	yes	complemented
270	C₂×C₁₉	—	2	1	no	—
271	C₂×C₁₉	—	2	1	no	—
272	C₂×C₁₉	—	2	2	no	—
273	C₂×C₁₉	—	8	4	no	—
274	C₂×C₁₉	—	8	4	no	—
275	C₂×C₁₉	#1598	1	4	yes	direct product factor
276	C₂×C₁₉	C₂×#447	1	1	yes	characteristic
277	C₂×C₁₉	C₂×#454	1	1	yes	characteristic
278	C₂×C₁₉	C₂×B(4,𝔽₂)	1	1	yes	characteristic
279	C₂⁵	—	2	1	no	—
280	C₂×#41	—	2	4	no	—
281	C₂×#41	—	2	4	no	—
282	C₂×#41	—	4	4	no	—
283	C₂×#41	—	4	4	no	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	2	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	—	4	4	no	—
292	C₂²×D₄	D₄×C₁₉	1	2	yes	—
293	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
297	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
299	C₂×D₈	—	2	8	no	—
300	C₂×D₈	—	4	8	no	—
301	C₂²×C₈	—	2	2	no	—
302	C₂²⋊Q₈	—	2	8	no	—
303	C₂²⋊Q₈	—	2	8	no	—
304	#121	—	2	4	no	—
305	#121	—	2	8	no	—
306	#121	—	2	8	no	—
307	#121	—	2	4	no	—
308	#121	—	2	2	no	—
309	#121	—	2	2	no	—
310	#121	D₄×C₁₉	1	4	yes	—
311	#121	C₂³×C₁₉	1	4	yes	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
316	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	4	no	—
321	C₂×C₂²⋊C₄	—	2	4	no	—
322	C₂×C₂²⋊C₄	—	4	4	no	—
323	C₂×C₂²⋊C₄	—	4	4	no	—
324	#102	—	2	8	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
327	#95	—	2	1	no	—
328	#95	C₂³×C₁₉	1	2	yes	—
329	C₁₉	C₂×#1598	1	1	yes	characteristic, direct product factor, Sylow
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	—	4	2	no	—
334	C₂⁴	—	4	2	no	—
335	C₂⁴	—	4	2	no	—
336	C₂⁴	—	4	1	no	—
337	C₂⁴	—	4	1	no	—
338	C₂⁴	—	4	2	no	—
339	C₂⁴	—	4	2	no	—
340	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
341	#41	—	4	16	no	—
342	#41	—	4	8	no	—
343	#41	—	4	8	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	4	4	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	—	4	8	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	4	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	8	2	no	—
363	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	8	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	D₈×C₁₉	1	4	yes	complemented
379	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
385	D₈	—	4	16	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	4	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	4	8	no	—
397	C₂²⋊C₄	—	4	8	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	4	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	8	no	—
407	C₂³	—	4	8	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	4	4	no	—
410	C₂³	—	4	4	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	—	8	4	no	—
417	C₂³	—	8	4	no	—
418	C₂³	—	8	2	no	—
419	C₂³	—	8	2	no	—
420	C₂³	—	8	2	no	—
421	C₂³	C₁₉×#120	1	1	yes	characteristic
422	C₂³	C₁₉×#120	1	1	yes	characteristic
423	C₂³	C₂×D₈×C₁₉	1	2	yes	—
424	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
425	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
426	Q₈	—	4	8	no	—
427	D₄	—	2	8	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	8	no	—
431	D₄	—	4	8	no	—
432	D₄	—	4	8	no	—
433	D₄	—	4	4	no	—
434	D₄	—	4	4	no	—
435	D₄	—	8	2	no	—
436	D₄	—	8	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	16	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	8	1	no	—
455	C₂×C₄	—	8	4	no	—
456	C₂×C₄	C₁₉×#120	1	2	yes	—
457	C₂×C₄	C₂×D₈×C₁₉	1	4	yes	complemented
458	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
459	C₈	—	4	4	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	8	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	8	no	—
478	C₂²	—	8	8	no	—
479	C₂²	C₁₉×#447	1	2	yes	—
480	C₂²	C₁₉×#447	1	2	yes	—
481	C₂²	C₁₉×#454	1	2	yes	—
482	C₂²	C₁₉×B(4,𝔽₂)	1	2	yes	—
483	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
484	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
485	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
486	C₄	—	2	4	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	8	2	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	—	2	2	no	—
495	C₂	—	8	4	no	—
496	C₂	—	8	4	no	—
497	C₂	C₁₉×#1598	1	4	yes	direct product factor
498	C₂	C₂×C₁₉×#447	1	1	yes	characteristic
499	C₂	C₂×C₁₉×#454	1	1	yes	characteristic
500	C₂	C₂×C₁₉×B(4,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#537	C₂	semidirect
2. C₂×C₁₉×#447	C₂	semidirect
3. C₂×C₁₉×#394	C₂	semidirect
4. C₁₉×#1598	C₂	direct (N × H)
5. C₂×C₁₉×#327	C₂	semidirect
6. C₂×C₁₉×#324	C₂	semidirect
12. C₁₉×#537	C₂²	semidirect
21. C₁₉×#447	C₂²	semidirect
25. C₁₉×#394	C₂²	semidirect
27. C₁₉×#327	C₂²	semidirect
28. C₁₉×#324	C₂²	semidirect
127. C₂²×C₄×C₁₉	D₈	semidirect
147. C₂×#1598	C₁₉	direct (N × H)
207. C₂×C₄×C₁₉	C₂×D₈	semidirect
210. C₂×#537	C₂×C₁₉	semidirect
211. C₂×#447	C₂×C₁₉	semidirect
212. C₂×#394	C₂×C₁₉	semidirect
213. #1598	C₂×C₁₉	direct (N × H)
214. C₂×#327	C₂×C₁₉	semidirect
215. C₂×#324	C₂×C₁₉	semidirect
253. #537	C₂²×C₁₉	semidirect
262. #447	C₂²×C₁₉	semidirect
266. #394	C₂²×C₁₉	semidirect
268. #327	C₂²×C₁₉	semidirect
269. #324	C₂²×C₁₉	semidirect
275. C₂×C₁₉	#1598	direct (N × H)
329. C₁₉	C₂×#1598	direct (N × H)
378. C₂²×C₄	D₈×C₁₉	semidirect
457. C₂×C₄	C₂×D₈×C₁₉	semidirect
497. C₂	C₁₉×#1598	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#537	2
C₂×C₁₉×#447	2
C₂×C₁₉×#394	2
C₁₉×#1598	2
C₂×C₁₉×#327	2
C₂×C₁₉×#324	2
C₂×#1598	19

Subgroups — C2×C19×#1598 #18024067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#1598 #18024067