Subgroups — #18088623

Order 4864.

730 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926586	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926502	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926308	C₂	1	1	yes	maximal, characteristic
5	#14563354	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926306	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂³×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926586	—	2	2	no	—
13	#11926586	C₄	1	4	yes	complemented
14	C₂×#10597275	—	2	1	no	—
15	C₂×#10597274	—	2	1	no	—
16	#11926502	—	2	2	no	—
17	#11926502	—	2	2	no	—
18	C₂×#10597272	—	2	1	no	—
19	C₂×C₈×Dic₁₉	—	2	1	no	—
20	#11926312	—	2	2	no	—
21	#11926308	C₄	1	4	yes	complemented
22	#11926306	—	2	1	no	—
23	#11926306	—	2	1	no	—
24	#11926306	—	2	1	no	—
25	#11926306	—	2	1	no	—
26	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₁₉×#343	C₄	1	4	yes	complemented
30	C₂³×C₄×C₁₉	—	2	1	no	—
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×Dic₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	—	2	1	no	—
39	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
41	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
44	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
45	C₂²×C₈×C₁₉	—	2	1	no	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
54	#10597372	—	2	1	no	—
55	#10597372	—	2	1	no	—
56	#10597372	C₂×C₄	1	2	yes	—
57	#10597372	D₄	1	2	yes	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	—	2	1	no	—
60	C₂×C₄⋊Dic₁₉	—	2	1	no	—
61	C₂×C₄⋊Dic₁₉	—	2	1	no	—
62	C₂×C₄⋊Dic₁₉	—	2	1	no	—
63	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
66	C₂×C₄×Dic₁₉	—	2	1	no	—
67	C₂×#64520	—	2	1	no	—
68	C₂×#64520	—	2	1	no	—
69	C₂×#64520	—	2	1	no	—
70	C₂×#64520	—	2	1	no	—
71	C₂×#64520	—	2	1	no	—
72	C₂×#64520	C₂×C₄	1	2	yes	—
73	C₂²×C₁₉⋊C₈	—	2	1	no	—
74	C₂²×C₁₉⋊C₈	—	2	1	no	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₂²×C₁₉⋊C₈	—	2	1	no	—
78	C₂²×C₁₉⋊C₈	C₂×C₄	1	2	yes	—
79	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
80	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
81	C₂²×C₁₉⋊C₈	Q₈	1	2	yes	—
82	#10597275	—	2	4	no	—
83	#10597274	—	2	4	no	—
84	#10597272	—	2	4	no	—
85	C₈×Dic₁₉	—	2	4	no	—
86	C₂⁴×C₁₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	—	2	2	no	—
88	C₂²×C₄×C₁₉	—	4	1	no	—
89	C₂²×C₄×C₁₉	—	4	1	no	—
90	C₂²×C₄×C₁₉	—	8	1	no	—
91	C₂²×C₄×C₁₉	—	8	1	no	—
92	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×Dic₁₉	—	2	1	no	—
107	C₂²×Dic₁₉	—	2	1	no	—
108	C₂²×Dic₁₉	—	2	2	no	—
109	C₂²×Dic₁₉	—	4	1	no	—
110	C₂²×Dic₁₉	—	4	1	no	—
111	C₂²×Dic₁₉	—	8	1	no	—
112	C₂²×Dic₁₉	—	8	1	no	—
113	M₁₆×C₁₉	—	2	2	no	—
114	M₁₆×C₁₉	—	2	2	no	—
115	M₁₆×C₁₉	—	2	2	no	—
116	M₁₆×C₁₉	—	2	2	no	—
117	M₁₆×C₁₉	—	2	2	no	—
118	M₁₆×C₁₉	—	2	2	no	—
119	M₁₆×C₁₉	C₄²	1	4	yes	—
120	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	—
121	C₂×C₈×C₁₉	—	2	2	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	2	2	no	—
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₄⋊C₄×C₁₉	—	2	2	no	—
128	C₄⋊C₄×C₁₉	—	2	2	no	—
129	C₄⋊C₄×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₂²⋊Dic₁₉	—	2	2	no	—
132	C₂²⋊Dic₁₉	—	2	2	no	—
133	C₄⋊Dic₁₉	—	2	1	no	—
134	C₄⋊Dic₁₉	—	2	1	no	—
135	C₄⋊Dic₁₉	—	2	2	no	—
136	C₄⋊Dic₁₉	—	2	2	no	—
137	C₄⋊Dic₁₉	—	4	1	no	—
138	C₄⋊Dic₁₉	—	4	1	no	—
139	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
140	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
141	C₄×Dic₁₉	—	2	2	no	—
142	C₄×Dic₁₉	—	2	2	no	—
143	#64520	—	2	2	no	—
144	#64520	—	2	2	no	—
145	#64520	—	4	1	no	—
146	#64520	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	2	2	no	—
148	C₂×C₁₉⋊C₈	—	2	2	no	—
149	C₂×C₁₉⋊C₈	—	2	1	no	—
150	C₂×C₁₉⋊C₈	—	2	1	no	—
151	C₂×C₁₉⋊C₈	—	2	2	no	—
152	C₂×C₁₉⋊C₈	—	2	2	no	—
153	C₂×C₁₉⋊C₈	—	2	1	no	—
154	C₂×C₁₉⋊C₈	—	2	1	no	—
155	C₂×C₁₉⋊C₈	—	2	2	no	—
156	C₂×C₁₉⋊C₈	—	4	1	no	—
157	C₂×C₁₉⋊C₈	—	4	1	no	—
158	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
159	C₂×C₁₉⋊C₈	C₄⋊C₄	1	2	yes	—
160	#10896	—	19	1	no	maximal, Sylow
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	2	1	no	—
163	C₂³×C₁₉	—	2	1	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	#117	1	1	yes	characteristic
166	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
168	C₂³×C₁₉	#121	1	1	yes	characteristic
169	C₂³×C₁₉	#123	1	1	yes	characteristic
170	C₂³×C₁₉	#125	1	1	yes	characteristic
171	C₂³×C₁₉	#126	1	1	yes	characteristic
172	C₂×C₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	8	2	no	—
174	C₂×C₄×C₁₉	—	8	1	no	—
175	C₂×C₄×C₁₉	—	8	1	no	—
176	C₂×C₄×C₁₉	—	8	2	no	—
177	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
200	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
201	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
202	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
205	C₂×Dic₁₉	—	2	2	no	—
206	C₂×Dic₁₉	—	2	2	no	—
207	C₂×Dic₁₉	—	4	1	no	—
208	C₂×Dic₁₉	—	4	1	no	—
209	C₂×Dic₁₉	—	4	1	no	—
210	C₂×Dic₁₉	—	4	1	no	—
211	C₂×Dic₁₉	—	4	2	no	—
212	C₂×Dic₁₉	—	8	2	no	—
213	C₂×Dic₁₉	—	8	1	no	—
214	C₂×Dic₁₉	—	8	1	no	—
215	C₂×Dic₁₉	—	8	2	no	—
216	C₈×C₁₉	—	2	4	no	—
217	C₈×C₁₉	—	2	4	no	—
218	C₁₉⋊C₈	—	2	2	no	—
219	C₁₉⋊C₈	—	2	2	no	—
220	C₁₉⋊C₈	—	4	2	no	—
221	C₂×#428	—	19	1	no	—
222	C₂×#405	—	19	1	no	—
223	C₂×#343	—	19	1	no	—
224	C₂×#343	D₁₉	1	1	yes	characteristic
225	C₂×#341	—	19	1	no	—
226	#1736	—	19	1	no	—
227	C₂×#340	—	19	1	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	1	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	2	1	no	—
237	C₂²×C₁₉	—	2	1	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
241	C₂²×C₁₉	#386	1	1	yes	characteristic
242	C₂²×C₁₉	#387	1	1	yes	characteristic
243	C₂²×C₁₉	#387	1	1	yes	characteristic
244	C₂²×C₁₉	#387	1	1	yes	characteristic
245	C₂²×C₁₉	#388	1	1	yes	characteristic
246	C₂²×C₁₉	#389	1	1	yes	characteristic
247	C₂²×C₁₉	#471	1	1	yes	characteristic
248	C₂²×C₁₉	#471	1	1	yes	characteristic
249	C₂²×C₁₉	#472	1	1	yes	characteristic
250	C₂²×C₁₉	#473	1	1	yes	characteristic
251	C₄×C₁₉	—	8	2	no	—
252	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
253	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
254	C₄×C₁₉	#385	1	1	yes	characteristic
255	C₄×C₁₉	#385	1	1	yes	characteristic
256	C₄×C₁₉	#387	1	1	yes	characteristic
257	C₄×C₁₉	#388	1	1	yes	characteristic
258	C₄×C₁₉	#389	1	1	yes	characteristic
259	C₄×C₁₉	#391	1	1	yes	characteristic
260	Dic₁₉	—	4	2	no	—
261	Dic₁₉	—	4	2	no	—
262	Dic₁₉	—	8	2	no	—
263	C₂²×M₁₆	—	19	1	no	—
264	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
265	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
266	C₂³×C₈	—	19	1	no	—
267	C₂×#117	—	19	1	no	—
268	C₂²×C₄⋊C₄	—	19	1	no	—
269	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
270	#428	—	19	4	no	—
271	#428	—	38	2	no	—
272	C₂×#107	—	38	1	no	—
273	C₂×#106	—	38	1	no	—
274	#405	—	38	2	no	—
275	#405	—	38	2	no	—
276	C₂×#97	—	38	1	no	—
277	C₂×C₄×C₈	—	38	1	no	—
278	#343	—	38	2	no	—
279	#343	Dic₁₉	1	4	yes	complemented
280	#341	—	19	4	no	—
281	#340	—	38	1	no	—
282	#340	—	38	1	no	—
283	#340	—	38	1	no	—
284	#340	—	38	1	no	—
285	C₂×C₁₉	—	2	1	no	—
286	C₂×C₁₉	—	2	1	no	—
287	C₂×C₁₉	—	2	1	no	—
288	C₂×C₁₉	—	2	1	no	—
289	C₂×C₁₉	#1436	1	1	yes	characteristic
290	C₂×C₁₉	#1907	1	1	yes	characteristic
291	C₂×C₁₉	#1908	1	1	yes	characteristic
292	C₂×C₁₉	#1930	1	1	yes	characteristic
293	C₂×C₁₉	#1931	1	1	yes	characteristic
294	C₂×C₁₉	#1951	1	1	yes	characteristic
295	C₂×C₁₉	#1952	1	1	yes	characteristic
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	38	1	no	—
298	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	2	1	no	—
305	C₂×M₁₆	—	19	2	no	—
306	C₂×M₁₆	—	38	1	no	—
307	C₂×M₁₆	—	38	1	no	—
308	C₂×M₁₆	—	38	1	no	—
309	C₂×M₁₆	—	38	1	no	—
310	C₂×M₁₆	—	38	1	no	—
311	C₂×M₁₆	Dic₃₈	1	2	yes	—
312	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
313	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
314	C₂×M₁₆	D₇₆	1	2	yes	—
315	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
316	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	—
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	—	2	1	no	—
319	C₂²×C₈	—	19	2	no	—
320	C₂²×C₈	—	19	1	no	—
321	C₂²×C₈	—	19	1	no	—
322	C₂²×C₈	—	19	2	no	—
323	C₂²×C₈	—	38	1	no	—
324	C₂²×C₈	—	38	1	no	—
325	C₂²×C₈	—	38	1	no	—
326	C₂²×C₈	—	38	1	no	—
327	C₂²×C₈	—	38	1	no	—
328	#117	—	19	2	no	—
329	#117	—	19	2	no	—
330	#117	—	38	1	no	—
331	#117	—	38	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	19	1	no	—
338	C₂×C₄⋊C₄	—	19	1	no	—
339	C₂×C₄⋊C₄	—	19	2	no	—
340	C₂×C₄⋊C₄	—	38	1	no	—
341	C₂×C₄⋊C₄	—	38	1	no	—
342	C₂×C₄⋊C₄	—	38	1	no	—
343	C₂×C₄⋊C₄	—	38	1	no	—
344	C₂×C₄⋊C₄	—	38	1	no	—
345	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
346	C₂×C₂²⋊C₄	—	38	1	no	—
347	C₂×C₄²	—	38	1	no	—
348	#107	—	38	4	no	—
349	#106	—	38	4	no	—
350	#97	—	38	4	no	—
351	C₄×C₈	—	38	4	no	—
352	C₁₉	#10896	1	1	yes	characteristic, complemented, Sylow
353	C₂⁴	#64541	1	1	yes	characteristic
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	4	1	no	—
357	C₂²×C₄	—	8	1	no	—
358	C₂²×C₄	—	8	1	no	—
359	C₂²×C₄	—	38	1	no	—
360	C₂²×C₄	—	38	1	no	—
361	C₂²×C₄	—	38	2	no	—
362	C₂²×C₄	—	76	1	no	—
363	C₂²×C₄	—	76	1	no	—
364	C₂²×C₄	—	152	1	no	—
365	C₂²×C₄	—	152	1	no	—
366	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
370	C₂²×C₄	#64541	1	1	yes	characteristic
371	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
372	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
373	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
374	C₂²×C₄	#64543	1	1	yes	characteristic
375	C₂²×C₄	#64543	1	1	yes	characteristic
376	C₂²×C₄	#64543	1	1	yes	characteristic
377	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
378	C₂²×C₄	#64545	1	1	yes	characteristic
379	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	38	2	no	—
387	M₁₆	—	38	2	no	—
388	M₁₆	—	76	1	no	—
389	M₁₆	—	76	1	no	—
390	M₁₆	C₄×Dic₁₉	1	4	yes	—
391	M₁₆	C₄⋊Dic₁₉	1	4	yes	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	19	2	no	—
399	C₂×C₈	—	19	2	no	—
400	C₂×C₈	—	38	2	no	—
401	C₂×C₈	—	38	2	no	—
402	C₂×C₈	—	38	1	no	—
403	C₂×C₈	—	38	1	no	—
404	C₂×C₈	—	38	1	no	—
405	C₂×C₈	—	38	1	no	—
406	C₂×C₈	—	38	2	no	—
407	C₂×C₈	—	38	2	no	—
408	C₂×C₈	—	38	2	no	—
409	C₂×C₈	—	76	1	no	—
410	C₂×C₈	—	76	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	19	2	no	—
416	C₄⋊C₄	—	19	2	no	—
417	C₄⋊C₄	—	38	1	no	—
418	C₄⋊C₄	—	38	1	no	—
419	C₄⋊C₄	—	38	2	no	—
420	C₄⋊C₄	—	38	2	no	—
421	C₄⋊C₄	—	76	1	no	—
422	C₄⋊C₄	—	76	1	no	—
423	C₂²⋊C₄	—	38	2	no	—
424	C₂²⋊C₄	—	38	2	no	—
425	C₄²	—	38	2	no	—
426	C₄²	—	38	2	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
432	C₂³	C₄×D₇₆	1	1	yes	characteristic
433	C₂³	#10597325	1	1	yes	characteristic
434	C₂³	#10597330	1	1	yes	characteristic
435	C₂³	#10597335	1	1	yes	characteristic
436	C₂³	#10597340	1	1	yes	characteristic
437	C₂³	#10597372	1	1	yes	characteristic
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	8	1	no	—
441	C₂×C₄	—	8	1	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	—	38	2	no	—
444	C₂×C₄	—	38	2	no	—
445	C₂×C₄	—	76	1	no	—
446	C₂×C₄	—	76	1	no	—
447	C₂×C₄	—	76	1	no	—
448	C₂×C₄	—	76	1	no	—
449	C₂×C₄	—	76	2	no	—
450	C₂×C₄	—	152	2	no	—
451	C₂×C₄	—	152	1	no	—
452	C₂×C₄	—	152	1	no	—
453	C₂×C₄	—	152	2	no	—
454	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
455	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
456	C₂×C₄	#10597323	1	1	yes	characteristic
457	C₂×C₄	#10597324	1	1	yes	characteristic
458	C₂×C₄	#10597324	1	1	yes	characteristic
459	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
460	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
461	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
462	C₂×C₄	#10597328	1	1	yes	characteristic
463	C₂×C₄	#10597329	1	1	yes	characteristic
464	C₂×C₄	#10597331	1	1	yes	characteristic
465	C₂×C₄	#10597332	1	1	yes	characteristic
466	C₂×C₄	#10597333	1	1	yes	characteristic
467	C₂×C₄	#10597334	1	1	yes	characteristic
468	C₂×C₄	#10597336	1	1	yes	characteristic
469	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
470	C₂×C₄	#10597338	1	1	yes	characteristic
471	C₂×C₄	#10597339	1	1	yes	characteristic
472	C₂×C₄	#10597341	1	1	yes	characteristic
473	C₂×C₄	#10597342	1	1	yes	characteristic
474	C₂×C₄	#10597343	1	1	yes	characteristic
475	C₂×C₄	#10597344	1	1	yes	characteristic
476	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
477	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
478	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
479	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
480	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
481	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
482	C₈	—	2	4	no	—
483	C₈	—	2	4	no	—
484	C₈	—	38	2	no	—
485	C₈	—	38	2	no	—
486	C₈	—	76	2	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
500	C₂²	#11926422	1	1	yes	characteristic
501	C₂²	#11926429	1	1	yes	characteristic
502	C₂²	#11926430	1	1	yes	characteristic
503	C₂²	#11926431	1	1	yes	characteristic
504	C₂²	#11926437	1	1	yes	characteristic
505	C₂²	#11926441	1	1	yes	characteristic
506	C₂²	#11926806	1	1	yes	characteristic
507	C₂²	#11926810	1	1	yes	characteristic
508	C₂²	#11926813	1	1	yes	characteristic
509	C₂²	#11926818	1	1	yes	characteristic
510	C₄	—	8	2	no	—
511	C₄	—	76	2	no	—
512	C₄	—	76	2	no	—
513	C₄	—	152	2	no	—
514	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
515	C₄	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
516	C₄	#11926418	1	1	yes	characteristic
517	C₄	#11926419	1	1	yes	characteristic
518	C₄	#11926427	1	1	yes	characteristic
519	C₄	#11926436	1	1	yes	characteristic
520	C₄	#11926443	1	1	yes	characteristic
521	C₄	#11926448	1	1	yes	characteristic
522	C₂	—	2	1	no	—
523	C₂	—	2	1	no	—
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	#14561869	1	1	yes	characteristic
527	C₂	#14564144	1	1	yes	characteristic
528	C₂	#14564151	1	1	yes	characteristic
529	C₂	#14564292	1	1	yes	characteristic
530	C₂	#14564299	1	1	yes	characteristic
531	C₂	#14564414	1	1	yes	characteristic
532	C₂	#14564419	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597330
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#343	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#343	D₁₉
hypocenter	C₁₉	#10896
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#343

Complements

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

N	H ≅ G/N	type
13. #11926586	C₄	semidirect
21. #11926308	C₄	semidirect
29. C₁₉×#343	C₄	semidirect
279. #343	Dic₁₉	semidirect
352. C₁₉	#10896	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926586	2
C₂×#11926502	2
C₂×#11926312	2
C₂×#11926308	2
#14563354	2
C₂×#11926306	2
C₂×C₁₉×#343	2
#10896	19