Subgroups — D₄×C₁₉×#101 #18028368

Order 4864.

1378 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	D₄×M₁₆×C₁₉	C₂	1	2	yes	maximal
3	C₂²×C₁₉×#101	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1966	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1901	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1784	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₉×#101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	—
11	D₄×Q₈×C₁₉	—	2	2	no	—
12	D₄×Q₈×C₁₉	—	2	4	no	—
13	D₄×Q₈×C₁₉	—	2	2	no	—
14	C₂×C₁₉×C₄⋊Q₈	C₄	1	2	yes	—
15	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊Q₈	C₄	1	4	yes	—
17	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₉	C₄	1	2	yes	—
20	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×#436	—	2	2	no	—
22	C₁₉×#435	—	2	4	no	—
23	C₈×D₄×C₁₉	—	2	2	no	—
24	C₁₉×#423	C₂²	1	2	yes	—
25	C₂×C₁₉×#101	—	2	8	no	—
26	C₂×C₁₉×#101	C₂²	1	4	yes	—
27	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#101	C₂²	1	2	yes	—
29	C₂×C₁₉×#101	C₂²	1	4	yes	—
30	C₂×C₁₉×#101	C₂²	1	1	yes	characteristic
31	C₁₉×#407	C₂²	1	4	yes	—
32	C₄×M₁₆×C₁₉	C₂²	1	2	yes	—
33	C₁₉×#343	C₂²	1	2	yes	—
34	C₁₉×#343	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₉	—	2	4	no	—
36	C₂²×Q₈×C₁₉	—	2	4	no	—
37	C₂²×Q₈×C₁₉	—	2	4	no	—
38	C₂²×Q₈×C₁₉	—	2	4	no	—
39	C₂²×Q₈×C₁₉	—	4	4	no	—
40	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
41	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
42	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
46	C₂×M₁₆×C₁₉	—	2	4	no	—
47	C₂×M₁₆×C₁₉	—	2	8	no	—
48	C₂×M₁₆×C₁₉	—	4	4	no	—
49	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
50	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
51	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₉	—	2	4	no	—
53	C₁₉×C₄⋊Q₈	—	2	4	no	—
54	C₁₉×C₄⋊Q₈	—	2	4	no	—
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	—	2	2	no	—
57	C₁₉×C₂²⋊Q₈	—	2	4	no	—
58	C₁₉×C₂²⋊Q₈	—	2	4	no	—
59	C₁₉×C₂²⋊Q₈	—	2	8	no	—
60	C₁₉×C₂²⋊Q₈	—	2	8	no	—
61	C₄×Q₈×C₁₉	—	2	2	no	—
62	C₄×Q₈×C₁₉	—	2	2	no	—
63	C₄×D₄×C₁₉	—	2	4	no	—
64	C₄×D₄×C₁₉	—	2	2	no	—
65	C₄×D₄×C₁₉	—	2	2	no	—
66	C₄×D₄×C₁₉	D₄	1	2	yes	—
67	C₄×D₄×C₁₉	D₄	1	4	yes	—
68	C₄×D₄×C₁₉	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×C₄⋊C₈	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	2	no	—
81	C₁₉×#101	—	2	4	no	—
82	C₁₉×#101	—	2	2	no	—
83	C₁₉×#101	—	2	8	no	—
84	C₁₉×#101	—	4	4	no	—
85	C₁₉×#101	D₄	1	4	yes	direct product factor
86	C₁₉×C₂²⋊C₈	—	2	4	no	—
87	C₁₉×C₂²⋊C₈	—	2	4	no	—
88	C₁₉×#97	—	2	2	no	—
89	C₄×C₈×C₁₉	—	2	2	no	—
90	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
91	C₂×Q₈×C₁₉	—	2	8	no	—
92	C₂×Q₈×C₁₉	—	2	8	no	—
93	C₂×Q₈×C₁₉	—	2	2	no	—
94	C₂×Q₈×C₁₉	—	2	4	no	—
95	C₂×Q₈×C₁₉	—	2	2	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	4	no	—
99	C₂×Q₈×C₁₉	—	4	4	no	—
100	C₂×Q₈×C₁₉	—	4	8	no	—
101	C₂×Q₈×C₁₉	—	4	8	no	—
102	C₂×Q₈×C₁₉	—	4	8	no	—
103	C₂×Q₈×C₁₉	—	4	8	no	—
104	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₁₉	#41	1	2	yes	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
108	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×D₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	4	no	—
115	C₂²×C₄×C₁₉	—	2	8	no	—
116	C₂²×C₄×C₁₉	—	4	4	no	—
117	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
126	M₁₆×C₁₉	—	2	2	no	—
127	M₁₆×C₁₉	—	2	4	no	—
128	M₁₆×C₁₉	—	2	2	no	—
129	M₁₆×C₁₉	—	2	4	no	—
130	M₁₆×C₁₉	—	2	2	no	—
131	M₁₆×C₁₉	—	4	8	no	—
132	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
133	C₂×C₈×C₁₉	—	2	2	no	—
134	C₂×C₈×C₁₉	—	2	4	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	4	8	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	8	no	—
141	C₄⋊C₄×C₁₉	—	2	4	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
144	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
145	C₂²⋊C₄×C₁₉	—	2	4	no	—
146	C₂²⋊C₄×C₁₉	—	2	4	no	—
147	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
148	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	C₂×D₄	1	2	yes	—
152	C₄²×C₁₉	C₂×D₄	1	2	yes	—
153	D₄×#101	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂³×C₁₉	—	2	2	no	—
155	C₂³×C₁₉	—	2	2	no	—
156	C₂³×C₁₉	—	2	4	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂³×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
161	Q₈×C₁₉	—	2	4	no	—
162	Q₈×C₁₉	—	2	4	no	—
163	Q₈×C₁₉	—	4	16	no	—
164	Q₈×C₁₉	—	4	4	no	—
165	Q₈×C₁₉	—	4	4	no	—
166	D₄×C₁₉	—	2	4	no	—
167	D₄×C₁₉	—	2	2	no	—
168	D₄×C₁₉	#101	1	4	yes	direct product factor
169	C₂×C₄×C₁₉	—	2	2	no	—
170	C₂×C₄×C₁₉	—	2	2	no	—
171	C₂×C₄×C₁₉	—	2	2	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	4	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	4	no	—
180	C₂×C₄×C₁₉	—	2	4	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	8	no	—
184	C₂×C₄×C₁₉	—	4	8	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₄×D₄	1	4	yes	—
191	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
195	C₈×C₁₉	—	2	4	no	—
196	C₈×C₁₉	—	4	4	no	—
197	C₈×C₁₉	—	4	2	no	—
198	C₂×D₄×Q₈	C₂×C₁₉	1	1	yes	characteristic
199	D₄×M₁₆	C₂×C₁₉	1	2	yes	—
200	C₂²×#101	C₂×C₁₉	1	2	yes	complemented
201	#1966	C₂×C₁₉	1	2	yes	complemented
202	#1901	C₂×C₁₉	1	4	yes	complemented
203	#1801	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#1784	C₂×C₁₉	1	2	yes	complemented
205	C₄×#101	C₂×C₁₉	1	1	yes	characteristic, complemented
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	2	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	4	4	no	—
214	C₂²×C₁₉	—	4	4	no	—
215	C₂²×C₁₉	C₂×#101	1	4	yes	complemented
216	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
217	C₂²×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₁₉	#518	1	1	yes	characteristic
219	C₄×C₁₉	—	2	4	no	—
220	C₄×C₁₉	—	2	4	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	2	no	—
223	C₄×C₁₉	—	4	4	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	C₂×#101	1	2	yes	complemented
226	C₄×C₁₉	D₄²	1	2	yes	—
227	C₄×C₁₉	#546	1	2	yes	—
228	C₂³×Q₈	C₂²×C₁₉	1	2	yes	—
229	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
230	D₄×Q₈	—	2	2	no	—
231	D₄×Q₈	—	2	4	no	—
232	D₄×Q₈	—	2	2	no	—
233	C₂×C₄⋊Q₈	C₄×C₁₉	1	2	yes	—
234	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
235	C₂×C₂²⋊Q₈	C₄×C₁₉	1	4	yes	—
236	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
237	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
238	C₂×C₄×D₄	C₄×C₁₉	1	2	yes	—
239	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
240	#436	—	2	2	no	—
241	#435	—	2	4	no	—
242	C₈×D₄	—	2	2	no	—
243	#423	C₂²×C₁₉	1	2	yes	—
244	C₂×#101	—	2	8	no	—
245	C₂×#101	C₂²×C₁₉	1	2	yes	—
246	C₂×#101	C₂²×C₁₉	1	4	yes	—
247	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
248	C₂×#101	C₂²×C₁₉	1	4	yes	—
249	C₂×#101	C₂²×C₁₉	1	1	yes	characteristic
250	#407	C₂²×C₁₉	1	4	yes	—
251	C₄×M₁₆	C₂²×C₁₉	1	2	yes	—
252	#343	C₂²×C₁₉	1	2	yes	—
253	#343	C₂²×C₁₉	1	2	yes	—
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	4	no	—
257	C₂×C₁₉	—	4	2	no	—
258	C₂×C₁₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₁₉	C₂²×#101	1	1	yes	characteristic
260	C₂×C₁₉	#2889	1	1	yes	characteristic
261	C₂²×Q₈	—	2	4	no	—
262	C₂²×Q₈	—	2	4	no	—
263	C₂²×Q₈	—	2	4	no	—
264	C₂²×Q₈	—	2	4	no	—
265	C₂²×Q₈	—	4	4	no	—
266	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	—
267	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
268	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
269	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
270	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
271	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
272	C₂×M₁₆	—	2	4	no	—
273	C₂×M₁₆	—	2	8	no	—
274	C₂×M₁₆	—	4	4	no	—
275	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
276	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
277	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
278	C₂²×C₈	—	2	4	no	—
279	C₄⋊Q₈	—	2	4	no	—
280	C₄⋊Q₈	—	2	4	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₂²⋊Q₈	—	2	4	no	—
284	C₂²⋊Q₈	—	2	4	no	—
285	C₂²⋊Q₈	—	2	8	no	—
286	C₂²⋊Q₈	—	2	8	no	—
287	C₄×Q₈	—	2	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	—	2	2	no	—
292	C₄×D₄	D₄×C₁₉	1	2	yes	—
293	C₄×D₄	D₄×C₁₉	1	4	yes	—
294	C₄×D₄	D₄×C₁₉	1	2	yes	—
295	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
296	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
297	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
303	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
304	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	#101	—	2	4	no	—
308	#101	—	2	2	no	—
309	#101	—	2	8	no	—
310	#101	—	4	4	no	—
311	#101	D₄×C₁₉	1	4	yes	direct product factor
312	C₂²⋊C₈	—	2	4	no	—
313	C₂²⋊C₈	—	2	4	no	—
314	#97	—	2	2	no	—
315	C₄×C₈	—	2	2	no	—
316	C₁₉	D₄×#101	1	1	yes	characteristic, direct product factor, Sylow
317	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
318	C₂×Q₈	—	2	8	no	—
319	C₂×Q₈	—	2	8	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	—	4	8	no	—
328	C₂×Q₈	—	4	8	no	—
329	C₂×Q₈	—	4	8	no	—
330	C₂×Q₈	—	4	8	no	—
331	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
332	C₂×Q₈	#41×C₁₉	1	2	yes	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
335	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
336	C₂×D₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
345	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
347	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
349	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
351	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
352	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	4	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	4	no	—
358	M₁₆	—	4	8	no	—
359	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	4	8	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
371	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
375	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	C₂×D₄×C₁₉	1	2	yes	—
379	C₄²	C₂×D₄×C₁₉	1	2	yes	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
385	C₂³	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
386	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
387	Q₈	—	2	4	no	—
388	Q₈	—	2	4	no	—
389	Q₈	—	4	16	no	—
390	Q₈	—	4	4	no	—
391	Q₈	—	4	4	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	2	no	—
394	D₄	C₁₉×#101	1	4	yes	direct product factor
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
413	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
414	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
415	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
416	C₂×C₄	C₄×D₄×C₁₉	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
419	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
420	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
421	C₈	—	2	4	no	—
422	C₈	—	4	4	no	—
423	C₈	—	4	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	C₂×C₁₉×#101	1	4	yes	complemented
434	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
435	C₂²	C₂×C₄×D₄×C₁₉	1	1	yes	characteristic
436	C₂²	C₁₉×#518	1	1	yes	characteristic
437	C₄	—	2	4	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	2	no	—
443	C₄	C₂×C₁₉×#101	1	2	yes	complemented
444	C₄	D₄²×C₁₉	1	2	yes	—
445	C₄	C₁₉×#546	1	2	yes	—
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	2	4	no	—
449	C₂	—	4	2	no	—
450	C₂	D₄×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
451	C₂	C₂²×C₁₉×#101	1	1	yes	characteristic
452	C₂	C₁₉×#2889	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×D₄×C₁₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄×D₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₁₉×#101	C₂	semidirect
4. C₁₉×#1966	C₂	semidirect
5. C₁₉×#1901	C₂	semidirect
6. C₁₉×#1801	C₂	semidirect
7. C₁₉×#1784	C₂	semidirect
8. C₄×C₁₉×#101	C₂	semidirect
85. C₁₉×#101	D₄	direct (N × H)
153. D₄×#101	C₁₉	direct (N × H)
168. D₄×C₁₉	#101	direct (N × H)
200. C₂²×#101	C₂×C₁₉	semidirect
201. #1966	C₂×C₁₉	semidirect
202. #1901	C₂×C₁₉	semidirect
203. #1801	C₂×C₁₉	semidirect
204. #1784	C₂×C₁₉	semidirect
205. C₄×#101	C₂×C₁₉	semidirect
215. C₂²×C₁₉	C₂×#101	semidirect
225. C₄×C₁₉	C₂×#101	semidirect
311. #101	D₄×C₁₉	direct (N × H)
316. C₁₉	D₄×#101	direct (N × H)
394. D₄	C₁₉×#101	direct (N × H)
433. C₂²	C₂×C₁₉×#101	semidirect
443. C₄	C₂×C₁₉×#101	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₁₉	2
D₄×M₁₆×C₁₉	2
C₂²×C₁₉×#101	2
C₁₉×#1966	2
C₁₉×#1901	2
C₁₉×#1801	2
C₁₉×#1784	2
C₄×C₁₉×#101	2
D₄×#101	19

Subgroups — D4×C19×#101 #18028368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₉×#101 #18028368