Subgroups — C₂×C₁₉×#3038 #18066371

Order 4864.

3478 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3038	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₉×#460	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₉×#459	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₉×#418	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₁₉	—	2	2	no	—
11	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
12	C₂×C₁₉×AGL(1,ℤ/8)	—	2	16	no	—
13	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	16	yes	complemented
14	C₂²×SD₁₆×C₁₉	C₂²	1	4	yes	complemented
15	C₂²×D₈×C₁₉	C₂²	1	4	yes	complemented
16	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
17	C₂×C₁₉×#127	—	2	1	no	—
18	C₂×C₁₉×#127	—	2	1	no	—
19	C₂×C₁₉×#127	—	2	4	no	—
20	C₂×C₁₉×#127	C₂²	1	4	yes	—
21	C₂×C₁₉×#127	C₂²	1	8	yes	complemented
22	C₄×#41×C₁₉	—	2	4	no	—
23	C₄×#41×C₁₉	C₂²	1	8	yes	complemented
24	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	complemented
25	C₂×C₄×D₄×C₁₉	—	2	2	no	—
26	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	complemented
27	C₂×C₁₉×#117	—	2	1	no	—
28	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₉	—	2	1	no	—
30	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
31	C₁₉×#460	C₂²	1	32	yes	complemented
32	C₁₉×#459	C₂²	1	32	yes	complemented
33	C₁₉×#423	C₂²	1	8	yes	complemented
34	C₂×C₁₉×C₄⋊C₈	C₂²	1	4	yes	complemented
35	C₁₉×#418	C₂²	1	16	yes	complemented
36	C₂×C₁₉×#102	C₂²	1	8	yes	complemented
37	C₂⁵×C₁₉	—	2	2	no	—
38	C₂×#41×C₁₉	—	2	2	no	—
39	C₂×#41×C₁₉	—	2	4	no	—
40	C₂×#41×C₁₉	D₄	1	8	yes	complemented
41	C₂×#41×C₁₉	C₂³	1	4	yes	—
42	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	—	2	1	no	—
44	C₂²×D₄×C₁₉	—	2	8	no	—
45	C₂²×D₄×C₁₉	—	2	4	no	—
46	C₂²×D₄×C₁₉	—	2	2	no	—
47	C₂²×D₄×C₁₉	—	2	4	no	—
48	C₂²×D₄×C₁₉	—	2	4	no	—
49	C₂²×D₄×C₁₉	—	2	16	no	—
50	C₂²×D₄×C₁₉	—	2	8	no	—
51	C₂²×D₄×C₁₉	—	4	16	no	—
52	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
53	C₂²×D₄×C₁₉	C₂³	1	8	yes	—
54	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₉	—	2	1	no	—
56	C₂³×C₄×C₁₉	—	2	2	no	—
57	C₂³×C₄×C₁₉	D₄	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₁₉×AGL(1,ℤ/8)	—	2	64	no	—
60	C₂×SD₁₆×C₁₉	—	2	16	no	—
61	C₂×SD₁₆×C₁₉	C₂³	1	16	yes	complemented
62	C₂×D₈×C₁₉	—	2	16	no	—
63	C₂×D₈×C₁₉	C₂³	1	16	yes	complemented
64	C₂×M₁₆×C₁₉	—	2	8	no	—
65	C₂×M₁₆×C₁₉	C₂³	1	8	yes	—
66	C₂²×C₈×C₁₉	C₂³	1	4	yes	—
67	C₁₉×#127	—	2	8	no	—
68	C₁₉×#127	—	2	8	no	—
69	C₁₉×#127	—	2	8	no	—
70	C₁₉×#127	C₂³	1	16	yes	—
71	C₄×Q₈×C₁₉	—	2	4	no	—
72	C₄×Q₈×C₁₉	C₂³	1	8	yes	complemented
73	C₄×D₄×C₁₉	—	2	16	no	—
74	C₄×D₄×C₁₉	—	2	4	no	—
75	C₄×D₄×C₁₉	C₂³	1	8	yes	complemented
76	C₁₉×#117	—	2	2	no	—
77	C₁₉×#117	—	2	8	no	—
78	C₁₉×#117	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄²×C₁₉	—	2	2	no	—
85	C₂×C₄²×C₁₉	—	2	8	no	—
86	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	D₄	1	4	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
91	C₁₉×C₄⋊C₈	C₂³	1	16	yes	complemented
92	C₁₉×#102	C₂³	1	32	yes	complemented
93	C₂⁴×C₁₉	—	2	1	no	—
94	C₂⁴×C₁₉	—	2	8	no	—
95	C₂⁴×C₁₉	—	2	4	no	—
96	C₂⁴×C₁₉	—	4	16	no	—
97	C₂⁴×C₁₉	—	4	8	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
99	#41×C₁₉	—	2	16	no	—
100	#41×C₁₉	—	2	8	no	—
101	#41×C₁₉	C₂×D₄	1	16	yes	complemented
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	complemented
105	C₂×Q₈×C₁₉	C₂⁴	1	2	yes	—
106	C₂×D₄×C₁₉	—	2	8	no	—
107	C₂×D₄×C₁₉	—	2	4	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	8	no	—
110	C₂×D₄×C₁₉	—	2	16	no	—
111	C₂×D₄×C₁₉	—	2	8	no	—
112	C₂×D₄×C₁₉	—	2	4	no	—
113	C₂×D₄×C₁₉	—	2	16	no	—
114	C₂×D₄×C₁₉	—	2	16	no	—
115	C₂×D₄×C₁₉	—	2	2	no	—
116	C₂×D₄×C₁₉	—	2	8	no	—
117	C₂×D₄×C₁₉	—	2	16	no	—
118	C₂×D₄×C₁₉	—	4	16	no	—
119	C₂×D₄×C₁₉	—	4	64	no	—
120	C₂×D₄×C₁₉	—	4	8	no	—
121	C₂×D₄×C₁₉	—	4	16	no	—
122	C₂×D₄×C₁₉	—	4	16	no	—
123	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	complemented
124	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
125	C₂×D₄×C₁₉	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	8	no	—
128	C₂²×C₄×C₁₉	—	2	8	no	—
129	C₂²×C₄×C₁₉	—	2	4	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	—	2	8	no	—
132	C₂²×C₄×C₁₉	—	4	8	no	—
133	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
134	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₉	#41	1	4	yes	—
140	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
142	SD₁₆×C₁₉	—	2	32	no	—
143	D₈×C₁₉	—	2	32	no	—
144	M₁₆×C₁₉	—	2	16	no	—
145	C₂×C₈×C₁₉	—	2	8	no	—
146	C₂×C₈×C₁₉	C₂⁴	1	8	yes	—
147	C₄⋊C₄×C₁₉	—	2	8	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	C₂⁴	1	4	yes	—
150	C₂²⋊C₄×C₁₉	—	2	4	no	—
151	C₂²⋊C₄×C₁₉	—	2	8	no	—
152	C₄²×C₁₉	—	2	4	no	—
153	C₄²×C₁₉	—	2	8	no	—
154	C₄²×C₁₉	C₂×D₄	1	4	yes	—
155	C₄²×C₁₉	C₂×D₄	1	4	yes	—
156	C₄²×C₁₉	C₂×D₄	1	4	yes	—
157	C₄²×C₁₉	C₂⁴	1	4	yes	—
158	C₂×#3038	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	4	no	—
160	C₂³×C₁₉	—	2	4	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	8	no	—
163	C₂³×C₁₉	—	4	32	no	—
164	C₂³×C₁₉	—	4	4	no	—
165	C₂³×C₁₉	—	4	16	no	—
166	C₂³×C₁₉	—	4	8	no	—
167	C₂³×C₁₉	—	4	16	no	—
168	C₂³×C₁₉	—	8	32	no	—
169	C₂³×C₁₉	#121	1	4	yes	—
170	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
171	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₁₉	—	2	4	no	—
173	Q₈×C₁₉	—	2	2	no	—
174	Q₈×C₁₉	C₂²×D₄	1	4	yes	complemented
175	D₄×C₁₉	—	2	16	no	—
176	D₄×C₁₉	—	2	4	no	—
177	D₄×C₁₉	—	2	8	no	—
178	D₄×C₁₉	—	2	2	no	—
179	D₄×C₁₉	—	2	8	no	—
180	D₄×C₁₉	—	4	32	no	—
181	D₄×C₁₉	—	4	16	no	—
182	D₄×C₁₉	—	4	8	no	—
183	D₄×C₁₉	—	4	32	no	—
184	D₄×C₁₉	C₂²×D₄	1	4	yes	complemented
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	16	no	—
189	C₂×C₄×C₁₉	—	2	16	no	—
190	C₂×C₄×C₁₉	—	2	4	no	—
191	C₂×C₄×C₁₉	—	4	4	no	—
192	C₂×C₄×C₁₉	—	4	16	no	—
193	C₂×C₄×C₁₉	#121	1	4	yes	—
194	C₂×C₄×C₁₉	#121	1	8	yes	—
195	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	8	yes	complemented
196	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
203	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
204	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
205	C₈×C₁₉	—	2	8	no	—
206	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	2	yes	complemented
207	C₂²×#127	C₂×C₁₉	1	1	yes	characteristic, complemented
208	C₂×C₄×#41	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#3038	C₂×C₁₉	1	16	yes	direct product factor
210	C₂×#460	C₂×C₁₉	1	4	yes	complemented
211	C₂×#459	C₂×C₁₉	1	4	yes	complemented
212	C₂×#423	C₂×C₁₉	1	1	yes	characteristic, complemented
213	C₂×#418	C₂×C₁₉	1	2	yes	complemented
214	C₂²×C₁₉	—	2	8	no	—
215	C₂²×C₁₉	—	2	4	no	—
216	C₂²×C₁₉	—	2	4	no	—
217	C₂²×C₁₉	—	4	8	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	4	8	no	—
220	C₂²×C₁₉	—	4	16	no	—
221	C₂²×C₁₉	—	8	32	no	—
222	C₂²×C₁₉	—	8	16	no	—
223	C₂²×C₁₉	C₂×#121	1	4	yes	—
224	C₂²×C₁₉	C₂×#121	1	2	yes	—
225	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
226	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
227	C₄×C₁₉	—	2	4	no	—
228	C₄×C₁₉	—	2	4	no	—
229	C₄×C₁₉	—	4	4	no	—
230	C₄×C₁₉	C₂×#121	1	4	yes	—
231	C₄×C₁₉	C₂×#121	1	2	yes	—
232	C₄×C₁₉	C₂×AGL(1,ℤ/8)	1	8	yes	complemented
233	C₄×C₁₉	C₂³×D₄	1	1	yes	characteristic
234	C₄×C₁₉	C₂²×#41	1	1	yes	characteristic
235	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
236	C₂³×D₄	—	2	2	no	—
237	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
238	C₂×AGL(1,ℤ/8)	—	2	16	no	—
239	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	16	yes	complemented
240	C₂²×SD₁₆	C₂²×C₁₉	1	4	yes	complemented
241	C₂²×D₈	C₂²×C₁₉	1	4	yes	complemented
242	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
243	C₂×#127	—	2	1	no	—
244	C₂×#127	—	2	4	no	—
245	C₂×#127	—	2	1	no	—
246	C₂×#127	C₂²×C₁₉	1	4	yes	—
247	C₂×#127	C₂²×C₁₉	1	8	yes	complemented
248	C₄×#41	—	2	4	no	—
249	C₄×#41	C₂²×C₁₉	1	8	yes	complemented
250	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	complemented
251	C₂×C₄×D₄	—	2	2	no	—
252	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	complemented
253	C₂×#117	—	2	1	no	—
254	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
255	C₂²×C₄²	—	2	1	no	—
256	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
257	#460	C₂²×C₁₉	1	32	yes	complemented
258	#459	C₂²×C₁₉	1	32	yes	complemented
259	#423	C₂²×C₁₉	1	8	yes	complemented
260	C₂×C₄⋊C₈	C₂²×C₁₉	1	4	yes	complemented
261	#418	C₂²×C₁₉	1	16	yes	complemented
262	C₂×#102	C₂²×C₁₉	1	8	yes	complemented
263	C₂×C₁₉	—	2	4	no	—
264	C₂×C₁₉	—	4	4	no	—
265	C₂×C₁₉	—	8	8	no	—
266	C₂×C₁₉	#3038	1	4	yes	direct product factor
267	C₂×C₁₉	C₂²×#121	1	1	yes	characteristic
268	C₂×C₁₉	C₂²×AGL(1,ℤ/8)	1	2	yes	—
269	C₂⁵	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	D₄×C₁₉	1	8	yes	complemented
273	C₂×#41	C₂³×C₁₉	1	4	yes	—
274	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	—	2	8	no	—
277	C₂²×D₄	—	2	2	no	—
278	C₂²×D₄	—	2	4	no	—
279	C₂²×D₄	—	2	4	no	—
280	C₂²×D₄	—	2	4	no	—
281	C₂²×D₄	—	2	16	no	—
282	C₂²×D₄	—	2	8	no	—
283	C₂²×D₄	—	4	16	no	—
284	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
285	C₂²×D₄	C₂³×C₁₉	1	8	yes	—
286	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂³×C₄	—	2	1	no	—
288	C₂³×C₄	—	2	2	no	—
289	C₂³×C₄	D₄×C₁₉	1	2	yes	—
290	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
291	AGL(1,ℤ/8)	—	2	64	no	—
292	C₂×SD₁₆	—	2	16	no	—
293	C₂×SD₁₆	C₂³×C₁₉	1	16	yes	complemented
294	C₂×D₈	—	2	16	no	—
295	C₂×D₈	C₂³×C₁₉	1	16	yes	complemented
296	C₂×M₁₆	—	2	8	no	—
297	C₂×M₁₆	C₂³×C₁₉	1	8	yes	—
298	C₂²×C₈	C₂³×C₁₉	1	4	yes	—
299	#127	—	2	8	no	—
300	#127	—	2	8	no	—
301	#127	—	2	8	no	—
302	#127	C₂³×C₁₉	1	16	yes	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	C₂³×C₁₉	1	8	yes	complemented
305	C₄×D₄	—	2	16	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	C₂³×C₁₉	1	8	yes	complemented
308	#117	—	2	2	no	—
309	#117	—	2	8	no	—
310	#117	C₂³×C₁₉	1	4	yes	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	8	no	—
318	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
319	C₂×C₄²	D₄×C₁₉	1	4	yes	—
320	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
322	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
323	C₄⋊C₈	C₂³×C₁₉	1	16	yes	complemented
324	#102	C₂³×C₁₉	1	32	yes	complemented
325	C₁₉	C₂×#3038	1	1	yes	characteristic, direct product factor, Sylow
326	C₂⁴	—	2	1	no	—
327	C₂⁴	—	2	8	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	4	16	no	—
330	C₂⁴	—	4	8	no	—
331	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
332	#41	—	2	16	no	—
333	#41	—	2	8	no	—
334	#41	C₂×D₄×C₁₉	1	16	yes	complemented
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	complemented
338	C₂×Q₈	C₂⁴×C₁₉	1	2	yes	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	8	no	—
343	C₂×D₄	—	2	16	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	16	no	—
347	C₂×D₄	—	2	16	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	16	no	—
351	C₂×D₄	—	4	16	no	—
352	C₂×D₄	—	4	64	no	—
353	C₂×D₄	—	4	8	no	—
354	C₂×D₄	—	4	16	no	—
355	C₂×D₄	—	4	16	no	—
356	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	complemented
357	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
358	C₂×D₄	C₂⁴×C₁₉	1	2	yes	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	8	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	4	8	no	—
366	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
368	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
372	C₂²×C₄	#41×C₁₉	1	4	yes	—
373	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
374	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
375	SD₁₆	—	2	32	no	—
376	D₈	—	2	32	no	—
377	M₁₆	—	2	16	no	—
378	C₂×C₈	—	2	8	no	—
379	C₂×C₈	C₂⁴×C₁₉	1	8	yes	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	C₂⁴×C₁₉	1	4	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	8	no	—
387	C₄²	C₂×D₄×C₁₉	1	4	yes	—
388	C₄²	C₂×D₄×C₁₉	1	4	yes	—
389	C₄²	C₂×D₄×C₁₉	1	4	yes	—
390	C₄²	C₂⁴×C₁₉	1	4	yes	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	8	no	—
395	C₂³	—	4	32	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	16	no	—
398	C₂³	—	4	8	no	—
399	C₂³	—	4	16	no	—
400	C₂³	—	8	32	no	—
401	C₂³	C₁₉×#121	1	4	yes	—
402	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
403	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
404	Q₈	—	2	4	no	—
405	Q₈	—	2	2	no	—
406	Q₈	C₂²×D₄×C₁₉	1	4	yes	complemented
407	D₄	—	2	16	no	—
408	D₄	—	2	4	no	—
409	D₄	—	2	8	no	—
410	D₄	—	2	2	no	—
411	D₄	—	2	8	no	—
412	D₄	—	4	32	no	—
413	D₄	—	4	16	no	—
414	D₄	—	4	8	no	—
415	D₄	—	4	32	no	—
416	D₄	C₂²×D₄×C₁₉	1	4	yes	complemented
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	16	no	—
421	C₂×C₄	—	2	16	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	C₁₉×#121	1	4	yes	—
426	C₂×C₄	C₁₉×#121	1	8	yes	—
427	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	8	yes	complemented
428	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
433	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
434	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
435	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
436	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
437	C₈	—	2	8	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	8	no	—
444	C₂²	—	4	16	no	—
445	C₂²	—	8	32	no	—
446	C₂²	—	8	16	no	—
447	C₂²	C₂×C₁₉×#121	1	4	yes	—
448	C₂²	C₂×C₁₉×#121	1	2	yes	—
449	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	4	yes	—
450	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	—	2	4	no	—
453	C₄	—	4	4	no	—
454	C₄	C₂×C₁₉×#121	1	4	yes	—
455	C₄	C₂×C₁₉×#121	1	2	yes	—
456	C₄	C₂×C₁₉×AGL(1,ℤ/8)	1	8	yes	complemented
457	C₄	C₂³×D₄×C₁₉	1	1	yes	characteristic
458	C₄	C₂²×#41×C₁₉	1	1	yes	characteristic
459	C₂	—	2	4	no	—
460	C₂	—	4	4	no	—
461	C₂	—	8	8	no	—
462	C₂	C₁₉×#3038	1	4	yes	direct product factor
463	C₂	C₂²×C₁₉×#121	1	1	yes	characteristic
464	C₂	C₂²×C₁₉×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₁₉×#127	C₂	semidirect
3. C₂×C₄×#41×C₁₉	C₂	semidirect
4. C₁₉×#3038	C₂	direct (N × H)
5. C₂×C₁₉×#460	C₂	semidirect
6. C₂×C₁₉×#459	C₂	semidirect
7. C₂×C₁₉×#423	C₂	semidirect
8. C₂×C₁₉×#418	C₂	semidirect
13. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
14. C₂²×SD₁₆×C₁₉	C₂²	semidirect
15. C₂²×D₈×C₁₉	C₂²	semidirect
21. C₂×C₁₉×#127	C₂²	semidirect
23. C₄×#41×C₁₉	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₉	C₂²	semidirect
26. C₂×C₄×D₄×C₁₉	C₂²	semidirect
31. C₁₉×#460	C₂²	semidirect
32. C₁₉×#459	C₂²	semidirect
33. C₁₉×#423	C₂²	semidirect
34. C₂×C₁₉×C₄⋊C₈	C₂²	semidirect
35. C₁₉×#418	C₂²	semidirect
36. C₂×C₁₉×#102	C₂²	semidirect
40. C₂×#41×C₁₉	D₄	semidirect
61. C₂×SD₁₆×C₁₉	C₂³	semidirect
63. C₂×D₈×C₁₉	C₂³	semidirect
72. C₄×Q₈×C₁₉	C₂³	semidirect
75. C₄×D₄×C₁₉	C₂³	semidirect
91. C₁₉×C₄⋊C₈	C₂³	semidirect
92. C₁₉×#102	C₂³	semidirect
101. #41×C₁₉	C₂×D₄	semidirect
104. C₂×Q₈×C₁₉	C₂×D₄	semidirect
123. C₂×D₄×C₁₉	C₂×D₄	semidirect
158. C₂×#3038	C₁₉	direct (N × H)
174. Q₈×C₁₉	C₂²×D₄	semidirect
184. D₄×C₁₉	C₂²×D₄	semidirect
195. C₂×C₄×C₁₉	AGL(1,ℤ/8)	semidirect
206. C₂²×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
207. C₂²×#127	C₂×C₁₉	semidirect
208. C₂×C₄×#41	C₂×C₁₉	semidirect
209. #3038	C₂×C₁₉	direct (N × H)
210. C₂×#460	C₂×C₁₉	semidirect
211. C₂×#459	C₂×C₁₉	semidirect
212. C₂×#423	C₂×C₁₉	semidirect
213. C₂×#418	C₂×C₁₉	semidirect
232. C₄×C₁₉	C₂×AGL(1,ℤ/8)	semidirect
239. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
240. C₂²×SD₁₆	C₂²×C₁₉	semidirect
241. C₂²×D₈	C₂²×C₁₉	semidirect
247. C₂×#127	C₂²×C₁₉	semidirect
249. C₄×#41	C₂²×C₁₉	semidirect
250. C₂×C₄×Q₈	C₂²×C₁₉	semidirect
252. C₂×C₄×D₄	C₂²×C₁₉	semidirect
257. #460	C₂²×C₁₉	semidirect
258. #459	C₂²×C₁₉	semidirect
259. #423	C₂²×C₁₉	semidirect
260. C₂×C₄⋊C₈	C₂²×C₁₉	semidirect
261. #418	C₂²×C₁₉	semidirect
262. C₂×#102	C₂²×C₁₉	semidirect
266. C₂×C₁₉	#3038	direct (N × H)
272. C₂×#41	D₄×C₁₉	semidirect
293. C₂×SD₁₆	C₂³×C₁₉	semidirect
295. C₂×D₈	C₂³×C₁₉	semidirect
304. C₄×Q₈	C₂³×C₁₉	semidirect
307. C₄×D₄	C₂³×C₁₉	semidirect
323. C₄⋊C₈	C₂³×C₁₉	semidirect
324. #102	C₂³×C₁₉	semidirect
325. C₁₉	C₂×#3038	direct (N × H)
334. #41	C₂×D₄×C₁₉	semidirect
337. C₂×Q₈	C₂×D₄×C₁₉	semidirect
356. C₂×D₄	C₂×D₄×C₁₉	semidirect
406. Q₈	C₂²×D₄×C₁₉	semidirect
416. D₄	C₂²×D₄×C₁₉	semidirect
427. C₂×C₄	C₁₉×AGL(1,ℤ/8)	semidirect
456. C₄	C₂×C₁₉×AGL(1,ℤ/8)	semidirect
462. C₂	C₁₉×#3038	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×AGL(1,ℤ/8)	2
C₂²×C₁₉×#127	2
C₂×C₄×#41×C₁₉	2
C₁₉×#3038	2
C₂×C₁₉×#460	2
C₂×C₁₉×#459	2
C₂×C₁₉×#423	2
C₂×C₁₉×#418	2
C₂×#3038	19

Subgroups — C2×C19×#3038 #18066371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₉×#3038 #18066371