Subgroups — C₂²×C₁₉×#453 #18066337

Order 4864.

5670 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#453	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₁₉×#104	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₉×#100	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×H(5,𝔽₂)	—	2	12	no	—
8	C₂×C₁₉×H(5,𝔽₂)	—	2	6	no	—
9	C₂×C₁₉×H(5,𝔽₂)	C₂²	1	12	yes	complemented
10	C₂²×#41×C₁₉	—	2	2	no	—
11	C₂²×#41×C₁₉	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₉	—	2	2	no	—
13	C₂³×D₄×C₁₉	—	2	2	no	—
14	C₂³×D₄×C₁₉	—	2	2	no	—
15	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₉×AGL(1,ℤ/8)	—	2	12	no	—
18	C₂×C₁₉×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
19	C₂²×SD₁₆×C₁₉	—	2	2	no	—
20	C₂²×D₈×C₁₉	—	2	2	no	—
21	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	complemented
22	C₂×C₁₉×#127	—	2	6	no	—
23	C₂×C₁₉×#127	C₂²	1	12	yes	complemented
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#453	C₂²	1	64	yes	direct product factor
26	C₂×C₁₉×#104	C₂²	1	24	yes	complemented
27	C₂×C₁₉×#100	C₂²	1	12	yes	complemented
28	C₂⁵×C₁₉	—	2	2	no	—
29	C₂⁵×C₁₉	—	2	1	no	—
30	C₂⁵×C₁₉	D₄	1	2	yes	—
31	C₁₉×H(5,𝔽₂)	—	2	48	no	—
32	C₁₉×H(5,𝔽₂)	—	2	48	no	—
33	C₁₉×H(5,𝔽₂)	—	2	24	no	—
34	C₁₉×H(5,𝔽₂)	C₂³	1	16	yes	complemented
35	C₂×#41×C₁₉	—	2	24	no	—
36	C₂×#41×C₁₉	—	2	24	no	—
37	C₂×#41×C₁₉	—	2	6	no	—
38	C₂×#41×C₁₉	—	2	6	no	—
39	C₂×#41×C₁₉	D₄	1	12	yes	complemented
40	C₂×#41×C₁₉	C₂³	1	12	yes	—
41	C₂²×Q₈×C₁₉	D₄	1	2	yes	complemented
42	C₂²×D₄×C₁₉	—	2	4	no	—
43	C₂²×D₄×C₁₉	—	2	24	no	—
44	C₂²×D₄×C₁₉	—	2	24	no	—
45	C₂²×D₄×C₁₉	—	2	2	no	—
46	C₂²×D₄×C₁₉	—	2	24	no	—
47	C₂²×D₄×C₁₉	—	2	24	no	—
48	C₂²×D₄×C₁₉	—	2	24	no	—
49	C₂²×D₄×C₁₉	—	2	2	no	—
50	C₂²×D₄×C₁₉	—	2	6	no	—
51	C₂²×D₄×C₁₉	—	2	2	no	—
52	C₂²×D₄×C₁₉	—	2	6	no	—
53	C₂²×D₄×C₁₉	—	2	3	no	—
54	C₂²×D₄×C₁₉	—	4	16	no	—
55	C₂²×D₄×C₁₉	D₄	1	6	yes	—
56	C₂²×D₄×C₁₉	D₄	1	2	yes	complemented
57	C₂²×D₄×C₁₉	C₂³	1	6	yes	—
58	C₂²×D₄×C₁₉	C₂³	1	6	yes	complemented
59	C₂³×C₄×C₁₉	—	2	2	no	—
60	C₂³×C₄×C₁₉	—	2	1	no	—
61	C₂³×C₄×C₁₉	—	2	2	no	—
62	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
63	C₁₉×AGL(1,ℤ/8)	—	2	48	no	—
64	C₁₉×AGL(1,ℤ/8)	C₂³	1	32	yes	complemented
65	C₂×SD₁₆×C₁₉	—	2	24	no	—
66	C₂×D₈×C₁₉	—	2	24	no	—
67	C₂×M₁₆×C₁₉	—	2	6	no	—
68	C₂×M₁₆×C₁₉	C₂³	1	12	yes	complemented
69	C₂²×C₈×C₁₉	—	2	2	no	—
70	C₁₉×#127	—	2	24	no	—
71	C₁₉×#127	C₂³	1	16	yes	complemented
72	C₂×C₄²×C₁₉	—	2	3	no	—
73	C₂×C₄²×C₁₉	C₂³	1	6	yes	complemented
74	C₁₉×#104	C₂³	1	32	yes	complemented
75	C₁₉×#100	C₂³	1	16	yes	complemented
76	C₂⁴×C₁₉	—	2	24	no	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	2	no	—
79	C₂⁴×C₁₉	—	2	6	no	—
80	C₂⁴×C₁₉	—	2	6	no	—
81	C₂⁴×C₁₉	—	4	8	no	—
82	C₂⁴×C₁₉	—	4	8	no	—
83	C₂⁴×C₁₉	—	4	3	no	—
84	C₂⁴×C₁₉	—	4	1	no	—
85	C₂⁴×C₁₉	—	8	8	no	—
86	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂⁴×C₁₉	C₂×D₄	1	12	yes	—
88	#41×C₁₉	—	2	96	no	—
89	#41×C₁₉	—	2	32	no	—
90	#41×C₁₉	—	2	24	no	—
91	#41×C₁₉	—	2	12	no	—
92	#41×C₁₉	—	2	12	no	—
93	#41×C₁₉	C₂×D₄	1	24	yes	complemented
94	#41×C₁₉	C₂⁴	1	8	yes	—
95	C₂×Q₈×C₁₉	—	2	6	no	—
96	C₂×Q₈×C₁₉	C₂×D₄	1	12	yes	complemented
97	C₂×D₄×C₁₉	—	2	48	no	—
98	C₂×D₄×C₁₉	—	2	96	no	—
99	C₂×D₄×C₁₉	—	2	96	no	—
100	C₂×D₄×C₁₉	—	2	12	no	—
101	C₂×D₄×C₁₉	—	2	12	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	12	no	—
106	C₂×D₄×C₁₉	—	2	6	no	—
107	C₂×D₄×C₁₉	—	2	12	no	—
108	C₂×D₄×C₁₉	—	2	12	no	—
109	C₂×D₄×C₁₉	—	2	12	no	—
110	C₂×D₄×C₁₉	—	2	12	no	—
111	C₂×D₄×C₁₉	—	2	12	no	—
112	C₂×D₄×C₁₉	—	2	6	no	—
113	C₂×D₄×C₁₉	—	4	96	no	—
114	C₂×D₄×C₁₉	—	4	6	no	—
115	C₂×D₄×C₁₉	—	4	6	no	—
116	C₂×D₄×C₁₉	C₂×D₄	1	12	yes	—
117	C₂×D₄×C₁₉	C₂×D₄	1	12	yes	complemented
118	C₂×D₄×C₁₉	C₂⁴	1	4	yes	—
119	C₂×D₄×C₁₉	C₂⁴	1	4	yes	complemented
120	C₂²×C₄×C₁₉	—	2	24	no	—
121	C₂²×C₄×C₁₉	—	2	8	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	6	no	—
124	C₂²×C₄×C₁₉	—	2	12	no	—
125	C₂²×C₄×C₁₉	—	2	12	no	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	6	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	3	yes	—
130	SD₁₆×C₁₉	—	2	32	no	—
131	D₈×C₁₉	—	2	32	no	—
132	M₁₆×C₁₉	—	2	12	no	—
133	M₁₆×C₁₉	C₂⁴	1	8	yes	complemented
134	C₂×C₈×C₁₉	—	2	12	no	—
135	C₄²×C₁₉	—	2	6	no	—
136	C₄²×C₁₉	C₂⁴	1	4	yes	complemented
137	C₂²×#453	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	32	no	—
140	C₂³×C₁₉	—	2	12	no	—
141	C₂³×C₁₉	—	2	12	no	—
142	C₂³×C₁₉	—	2	12	no	—
143	C₂³×C₁₉	—	2	4	no	—
144	C₂³×C₁₉	—	4	24	no	—
145	C₂³×C₁₉	—	4	24	no	—
146	C₂³×C₁₉	—	4	8	no	—
147	C₂³×C₁₉	—	4	8	no	—
148	C₂³×C₁₉	—	4	6	no	—
149	C₂³×C₁₉	—	4	6	no	—
150	C₂³×C₁₉	—	8	12	no	—
151	C₂³×C₁₉	—	8	12	no	—
152	C₂³×C₁₉	—	8	48	no	—
153	C₂³×C₁₉	—	8	4	no	—
154	C₂³×C₁₉	#120	1	3	yes	—
155	C₂³×C₁₉	#120	1	1	yes	characteristic
156	C₂³×C₁₉	C₂²×D₄	1	3	yes	—
157	C₂³×C₁₉	C₂²×D₄	1	8	yes	—
158	Q₈×C₁₉	—	2	12	no	—
159	Q₈×C₁₉	C₂²×D₄	1	8	yes	complemented
160	D₄×C₁₉	—	2	64	no	—
161	D₄×C₁₉	—	2	24	no	—
162	D₄×C₁₉	—	2	8	no	—
163	D₄×C₁₉	—	2	24	no	—
164	D₄×C₁₉	—	2	12	no	—
165	D₄×C₁₉	—	2	8	no	—
166	D₄×C₁₉	—	2	8	no	—
167	D₄×C₁₉	—	4	64	no	—
168	D₄×C₁₉	—	4	12	no	—
169	D₄×C₁₉	C₂²×D₄	1	8	yes	complemented
170	C₂×C₄×C₁₉	—	2	32	no	—
171	C₂×C₄×C₁₉	—	2	24	no	—
172	C₂×C₄×C₁₉	—	2	12	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	24	no	—
175	C₂×C₄×C₁₉	—	2	8	no	—
176	C₂×C₄×C₁₉	#120	1	6	yes	—
177	C₂×C₄×C₁₉	#120	1	6	yes	—
178	C₂×C₄×C₁₉	C₂²×D₄	1	3	yes	—
179	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
180	C₂×C₄×C₁₉	C₂²×D₄	1	6	yes	—
181	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
182	C₈×C₁₉	—	2	8	no	—
183	C₂²×H(5,𝔽₂)	C₂×C₁₉	1	1	yes	characteristic, complemented
184	C₂²×AGL(1,ℤ/8)	C₂×C₁₉	1	2	yes	complemented
185	C₂²×#127	C₂×C₁₉	1	1	yes	characteristic, complemented
186	C₂×#453	C₂×C₁₉	1	24	yes	direct product factor
187	C₂²×#104	C₂×C₁₉	1	2	yes	complemented
188	C₂²×#100	C₂×C₁₉	1	1	yes	characteristic, complemented
189	C₂²×C₁₉	—	2	6	no	—
190	C₂²×C₁₉	—	2	6	no	—
191	C₂²×C₁₉	—	2	8	no	—
192	C₂²×C₁₉	—	2	8	no	—
193	C₂²×C₁₉	—	4	8	no	—
194	C₂²×C₁₉	—	4	8	no	—
195	C₂²×C₁₉	—	4	24	no	—
196	C₂²×C₁₉	—	4	24	no	—
197	C₂²×C₁₉	—	4	4	no	—
198	C₂²×C₁₉	—	8	12	no	—
199	C₂²×C₁₉	—	8	12	no	—
200	C₂²×C₁₉	—	8	32	no	—
201	C₂²×C₁₉	—	8	12	no	—
202	C₂²×C₁₉	#453	1	4	yes	direct product factor
203	C₂²×C₁₉	C₂×#120	1	3	yes	—
204	C₂²×C₁₉	C₂×#120	1	3	yes	—
205	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
206	C₄×C₁₉	—	2	8	no	—
207	C₄×C₁₉	—	2	8	no	—
208	C₄×C₁₉	C₂×#120	1	6	yes	—
209	C₄×C₁₉	C₂³×D₄	1	2	yes	—
210	C₂×H(5,𝔽₂)	—	2	12	no	—
211	C₂×H(5,𝔽₂)	—	2	6	no	—
212	C₂×H(5,𝔽₂)	C₂²×C₁₉	1	12	yes	complemented
213	C₂²×#41	—	2	2	no	—
214	C₂²×#41	C₂²×C₁₉	1	2	yes	—
215	C₂³×D₄	—	2	2	no	—
216	C₂³×D₄	—	2	2	no	—
217	C₂³×D₄	—	2	2	no	—
218	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
219	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic, complemented
220	C₂×AGL(1,ℤ/8)	—	2	12	no	—
221	C₂×AGL(1,ℤ/8)	C₂²×C₁₉	1	24	yes	complemented
222	C₂²×SD₁₆	—	2	2	no	—
223	C₂²×D₈	—	2	2	no	—
224	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	complemented
225	C₂×#127	—	2	6	no	—
226	C₂×#127	C₂²×C₁₉	1	12	yes	complemented
227	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic, complemented
228	#453	C₂²×C₁₉	1	64	yes	direct product factor
229	C₂×#104	C₂²×C₁₉	1	24	yes	complemented
230	C₂×#100	C₂²×C₁₉	1	12	yes	complemented
231	C₂×C₁₉	—	2	1	no	—
232	C₂×C₁₉	—	2	3	no	—
233	C₂×C₁₉	—	4	8	no	—
234	C₂×C₁₉	—	4	8	no	—
235	C₂×C₁₉	—	8	4	no	—
236	C₂×C₁₉	C₂×#453	1	6	yes	direct product factor
237	C₂×C₁₉	C₂²×#120	1	1	yes	characteristic
238	C₂⁵	—	2	2	no	—
239	C₂⁵	—	2	1	no	—
240	C₂⁵	D₄×C₁₉	1	2	yes	—
241	H(5,𝔽₂)	—	2	48	no	—
242	H(5,𝔽₂)	—	2	48	no	—
243	H(5,𝔽₂)	—	2	24	no	—
244	H(5,𝔽₂)	C₂³×C₁₉	1	16	yes	complemented
245	C₂×#41	—	2	24	no	—
246	C₂×#41	—	2	24	no	—
247	C₂×#41	—	2	6	no	—
248	C₂×#41	—	2	6	no	—
249	C₂×#41	D₄×C₁₉	1	12	yes	complemented
250	C₂×#41	C₂³×C₁₉	1	12	yes	—
251	C₂²×Q₈	D₄×C₁₉	1	2	yes	complemented
252	C₂²×D₄	—	2	4	no	—
253	C₂²×D₄	—	2	24	no	—
254	C₂²×D₄	—	2	24	no	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	—	2	24	no	—
257	C₂²×D₄	—	2	24	no	—
258	C₂²×D₄	—	2	24	no	—
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	—	2	6	no	—
261	C₂²×D₄	—	2	2	no	—
262	C₂²×D₄	—	2	6	no	—
263	C₂²×D₄	—	2	3	no	—
264	C₂²×D₄	—	4	16	no	—
265	C₂²×D₄	D₄×C₁₉	1	6	yes	—
266	C₂²×D₄	D₄×C₁₉	1	2	yes	complemented
267	C₂²×D₄	C₂³×C₁₉	1	6	yes	—
268	C₂²×D₄	C₂³×C₁₉	1	6	yes	complemented
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
273	AGL(1,ℤ/8)	—	2	48	no	—
274	AGL(1,ℤ/8)	C₂³×C₁₉	1	32	yes	complemented
275	C₂×SD₁₆	—	2	24	no	—
276	C₂×D₈	—	2	24	no	—
277	C₂×M₁₆	—	2	6	no	—
278	C₂×M₁₆	C₂³×C₁₉	1	12	yes	complemented
279	C₂²×C₈	—	2	2	no	—
280	#127	—	2	24	no	—
281	#127	C₂³×C₁₉	1	16	yes	complemented
282	C₂×C₄²	—	2	3	no	—
283	C₂×C₄²	C₂³×C₁₉	1	6	yes	complemented
284	#104	C₂³×C₁₉	1	32	yes	complemented
285	#100	C₂³×C₁₉	1	16	yes	complemented
286	C₁₉	C₂²×#453	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴	—	2	24	no	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	2	6	no	—
291	C₂⁴	—	2	6	no	—
292	C₂⁴	—	4	8	no	—
293	C₂⁴	—	4	8	no	—
294	C₂⁴	—	4	3	no	—
295	C₂⁴	—	4	1	no	—
296	C₂⁴	—	8	8	no	—
297	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
298	C₂⁴	C₂×D₄×C₁₉	1	12	yes	—
299	#41	—	2	96	no	—
300	#41	—	2	32	no	—
301	#41	—	2	24	no	—
302	#41	—	2	12	no	—
303	#41	—	2	12	no	—
304	#41	C₂×D₄×C₁₉	1	24	yes	complemented
305	#41	C₂⁴×C₁₉	1	8	yes	—
306	C₂×Q₈	—	2	6	no	—
307	C₂×Q₈	C₂×D₄×C₁₉	1	12	yes	complemented
308	C₂×D₄	—	2	48	no	—
309	C₂×D₄	—	2	96	no	—
310	C₂×D₄	—	2	96	no	—
311	C₂×D₄	—	2	12	no	—
312	C₂×D₄	—	2	12	no	—
313	C₂×D₄	—	2	32	no	—
314	C₂×D₄	—	2	32	no	—
315	C₂×D₄	—	2	32	no	—
316	C₂×D₄	—	2	12	no	—
317	C₂×D₄	—	2	6	no	—
318	C₂×D₄	—	2	12	no	—
319	C₂×D₄	—	2	12	no	—
320	C₂×D₄	—	2	12	no	—
321	C₂×D₄	—	2	12	no	—
322	C₂×D₄	—	2	12	no	—
323	C₂×D₄	—	2	6	no	—
324	C₂×D₄	—	4	96	no	—
325	C₂×D₄	—	4	6	no	—
326	C₂×D₄	—	4	6	no	—
327	C₂×D₄	C₂×D₄×C₁₉	1	12	yes	—
328	C₂×D₄	C₂×D₄×C₁₉	1	12	yes	complemented
329	C₂×D₄	C₂⁴×C₁₉	1	4	yes	—
330	C₂×D₄	C₂⁴×C₁₉	1	4	yes	complemented
331	C₂²×C₄	—	2	24	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	6	no	—
335	C₂²×C₄	—	2	12	no	—
336	C₂²×C₄	—	2	12	no	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	3	yes	—
338	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₉	1	6	yes	—
340	C₂²×C₄	C₂⁴×C₁₉	1	3	yes	—
341	SD₁₆	—	2	32	no	—
342	D₈	—	2	32	no	—
343	M₁₆	—	2	12	no	—
344	M₁₆	C₂⁴×C₁₉	1	8	yes	complemented
345	C₂×C₈	—	2	12	no	—
346	C₄²	—	2	6	no	—
347	C₄²	C₂⁴×C₁₉	1	4	yes	complemented
348	C₂³	—	2	4	no	—
349	C₂³	—	2	32	no	—
350	C₂³	—	2	12	no	—
351	C₂³	—	2	12	no	—
352	C₂³	—	2	12	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	4	24	no	—
355	C₂³	—	4	24	no	—
356	C₂³	—	4	8	no	—
357	C₂³	—	4	8	no	—
358	C₂³	—	4	6	no	—
359	C₂³	—	4	6	no	—
360	C₂³	—	8	12	no	—
361	C₂³	—	8	12	no	—
362	C₂³	—	8	48	no	—
363	C₂³	—	8	4	no	—
364	C₂³	C₁₉×#120	1	3	yes	—
365	C₂³	C₁₉×#120	1	1	yes	characteristic
366	C₂³	C₂²×D₄×C₁₉	1	3	yes	—
367	C₂³	C₂²×D₄×C₁₉	1	8	yes	—
368	Q₈	—	2	12	no	—
369	Q₈	C₂²×D₄×C₁₉	1	8	yes	complemented
370	D₄	—	2	64	no	—
371	D₄	—	2	24	no	—
372	D₄	—	2	8	no	—
373	D₄	—	2	24	no	—
374	D₄	—	2	12	no	—
375	D₄	—	2	8	no	—
376	D₄	—	2	8	no	—
377	D₄	—	4	64	no	—
378	D₄	—	4	12	no	—
379	D₄	C₂²×D₄×C₁₉	1	8	yes	complemented
380	C₂×C₄	—	2	32	no	—
381	C₂×C₄	—	2	24	no	—
382	C₂×C₄	—	2	12	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	24	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	C₁₉×#120	1	6	yes	—
387	C₂×C₄	C₁₉×#120	1	6	yes	—
388	C₂×C₄	C₂²×D₄×C₁₉	1	3	yes	—
389	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
390	C₂×C₄	C₂²×D₄×C₁₉	1	6	yes	—
391	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
392	C₈	—	2	8	no	—
393	C₂²	—	2	6	no	—
394	C₂²	—	2	6	no	—
395	C₂²	—	2	8	no	—
396	C₂²	—	2	8	no	—
397	C₂²	—	4	8	no	—
398	C₂²	—	4	8	no	—
399	C₂²	—	4	24	no	—
400	C₂²	—	4	24	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	8	12	no	—
403	C₂²	—	8	12	no	—
404	C₂²	—	8	32	no	—
405	C₂²	—	8	12	no	—
406	C₂²	C₁₉×#453	1	4	yes	direct product factor
407	C₂²	C₂×C₁₉×#120	1	3	yes	—
408	C₂²	C₂×C₁₉×#120	1	3	yes	—
409	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
410	C₄	—	2	8	no	—
411	C₄	—	2	8	no	—
412	C₄	C₂×C₁₉×#120	1	6	yes	—
413	C₄	C₂³×D₄×C₁₉	1	2	yes	—
414	C₂	—	2	1	no	—
415	C₂	—	2	3	no	—
416	C₂	—	4	8	no	—
417	C₂	—	4	8	no	—
418	C₂	—	8	4	no	—
419	C₂	C₂×C₁₉×#453	1	6	yes	direct product factor
420	C₂	C₂²×C₁₉×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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. C₂²×C₁₉×H(5,𝔽₂)	C₂	semidirect
2. C₂²×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
3. C₂²×C₁₉×#127	C₂	semidirect
4. C₂×C₁₉×#453	C₂	direct (N × H)
5. C₂²×C₁₉×#104	C₂	semidirect
6. C₂²×C₁₉×#100	C₂	semidirect
9. C₂×C₁₉×H(5,𝔽₂)	C₂²	semidirect
16. C₂³×D₄×C₁₉	C₂²	semidirect
18. C₂×C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂²×M₁₆×C₁₉	C₂²	semidirect
23. C₂×C₁₉×#127	C₂²	semidirect
24. C₂²×C₄²×C₁₉	C₂²	semidirect
25. C₁₉×#453	C₂²	direct (N × H)
26. C₂×C₁₉×#104	C₂²	semidirect
27. C₂×C₁₉×#100	C₂²	semidirect
34. C₁₉×H(5,𝔽₂)	C₂³	semidirect
39. C₂×#41×C₁₉	D₄	semidirect
41. C₂²×Q₈×C₁₉	D₄	semidirect
56. C₂²×D₄×C₁₉	D₄	semidirect
58. C₂²×D₄×C₁₉	C₂³	semidirect
64. C₁₉×AGL(1,ℤ/8)	C₂³	semidirect
68. C₂×M₁₆×C₁₉	C₂³	semidirect
71. C₁₉×#127	C₂³	semidirect
73. C₂×C₄²×C₁₉	C₂³	semidirect
74. C₁₉×#104	C₂³	semidirect
75. C₁₉×#100	C₂³	semidirect
93. #41×C₁₉	C₂×D₄	semidirect
96. C₂×Q₈×C₁₉	C₂×D₄	semidirect
117. C₂×D₄×C₁₉	C₂×D₄	semidirect
119. C₂×D₄×C₁₉	C₂⁴	semidirect
133. M₁₆×C₁₉	C₂⁴	semidirect
136. C₄²×C₁₉	C₂⁴	semidirect
137. C₂²×#453	C₁₉	direct (N × H)
159. Q₈×C₁₉	C₂²×D₄	semidirect
169. D₄×C₁₉	C₂²×D₄	semidirect
183. C₂²×H(5,𝔽₂)	C₂×C₁₉	semidirect
184. C₂²×AGL(1,ℤ/8)	C₂×C₁₉	semidirect
185. C₂²×#127	C₂×C₁₉	semidirect
186. C₂×#453	C₂×C₁₉	direct (N × H)
187. C₂²×#104	C₂×C₁₉	semidirect
188. C₂²×#100	C₂×C₁₉	semidirect
202. C₂²×C₁₉	#453	direct (N × H)
212. C₂×H(5,𝔽₂)	C₂²×C₁₉	semidirect
219. C₂³×D₄	C₂²×C₁₉	semidirect
221. C₂×AGL(1,ℤ/8)	C₂²×C₁₉	semidirect
224. C₂²×M₁₆	C₂²×C₁₉	semidirect
226. C₂×#127	C₂²×C₁₉	semidirect
227. C₂²×C₄²	C₂²×C₁₉	semidirect
228. #453	C₂²×C₁₉	direct (N × H)
229. C₂×#104	C₂²×C₁₉	semidirect
230. C₂×#100	C₂²×C₁₉	semidirect
236. C₂×C₁₉	C₂×#453	direct (N × H)
244. H(5,𝔽₂)	C₂³×C₁₉	semidirect
249. C₂×#41	D₄×C₁₉	semidirect
251. C₂²×Q₈	D₄×C₁₉	semidirect
266. C₂²×D₄	D₄×C₁₉	semidirect
268. C₂²×D₄	C₂³×C₁₉	semidirect
274. AGL(1,ℤ/8)	C₂³×C₁₉	semidirect
278. C₂×M₁₆	C₂³×C₁₉	semidirect
281. #127	C₂³×C₁₉	semidirect
283. C₂×C₄²	C₂³×C₁₉	semidirect
284. #104	C₂³×C₁₉	semidirect
285. #100	C₂³×C₁₉	semidirect
286. C₁₉	C₂²×#453	direct (N × H)
304. #41	C₂×D₄×C₁₉	semidirect
307. C₂×Q₈	C₂×D₄×C₁₉	semidirect
328. C₂×D₄	C₂×D₄×C₁₉	semidirect
330. C₂×D₄	C₂⁴×C₁₉	semidirect
344. M₁₆	C₂⁴×C₁₉	semidirect
347. C₄²	C₂⁴×C₁₉	semidirect
369. Q₈	C₂²×D₄×C₁₉	semidirect
379. D₄	C₂²×D₄×C₁₉	semidirect
406. C₂²	C₁₉×#453	direct (N × H)
419. C₂	C₂×C₁₉×#453	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×H(5,𝔽₂)	2
C₂²×C₁₉×AGL(1,ℤ/8)	2
C₂²×C₁₉×#127	2
C₂×C₁₉×#453	2
C₂²×C₁₉×#104	2
C₂²×C₁₉×#100	2
C₂²×#453	19

Subgroups — C22×C19×#453 #18066337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×#453 #18066337