Subgroups — #18090433

Order 4864.

778 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926567	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926443	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926313	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
6	#14563328	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	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₄	1	2	yes	—
11	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926567	—	2	2	no	—
14	#11926567	—	2	2	no	—
15	C₂×Dic₁₉⋊C₈	—	2	1	no	—
16	C₂×Dic₁₉⋊C₈	—	2	1	no	—
17	#11926443	—	2	1	no	—
18	#11926443	—	2	1	no	—
19	#11926443	—	2	1	no	—
20	#11926443	—	2	1	no	—
21	C₂×C₁₉⋊#95	C₄	1	2	yes	—
22	#11926313	—	2	2	no	—
23	#11926312	—	2	2	no	—
24	#11926312	—	2	2	no	—
25	#11926298	—	2	1	no	—
26	#11926298	—	2	1	no	—
27	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×#343	—	2	2	no	—
31	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
33	C₂³×Dic₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×Dic₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	—	2	1	no	—
43	C₂×M₁₆×C₁₉	—	2	1	no	—
44	C₂×M₁₆×C₁₉	—	2	1	no	—
45	C₂×M₁₆×C₁₉	—	2	1	no	—
46	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
47	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
48	C₂²×C₈×C₁₉	—	2	1	no	—
49	C₂²×C₈×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	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	Q₈	1	2	yes	—
56	C₂×C₄⋊Dic₁₉	—	2	1	no	—
57	C₂×C₄⋊Dic₁₉	—	2	1	no	—
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	2	no	—
63	C₂×C₄⋊Dic₁₉	—	2	2	no	—
64	C₂×C₄⋊Dic₁₉	—	4	4	no	—
65	C₂×C₄×Dic₁₉	—	2	1	no	—
66	C₂×C₄×Dic₁₉	—	2	1	no	—
67	C₂×C₄×Dic₁₉	—	2	1	no	—
68	C₂×C₄×Dic₁₉	—	2	1	no	—
69	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
70	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
71	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
72	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	—	2	1	no	—
75	C₂×#64520	—	2	1	no	—
76	C₂×#64520	—	2	1	no	—
77	C₂×#64520	—	2	1	no	—
78	C₂×#64520	—	2	1	no	—
79	C₂×#64520	—	2	1	no	—
80	C₂×#64520	—	2	1	no	—
81	C₂×#64520	—	2	1	no	—
82	C₂×#64520	—	2	1	no	—
83	C₂×#64520	D₄	1	2	yes	—
84	C₂×#64520	Q₈	1	2	yes	—
85	C₂²×C₁₉⋊C₈	—	2	1	no	—
86	C₂²×C₁₉⋊C₈	—	2	1	no	—
87	C₁₉⋊#95	—	2	2	no	—
88	C₁₉⋊#95	—	2	2	no	—
89	Dic₁₉⋊C₈	—	2	4	no	—
90	Dic₁₉⋊C₈	—	2	4	no	—
91	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	2	2	no	—
94	C₂²×C₄×C₁₉	—	4	2	no	—
95	C₂²×C₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	C₄⋊C₄	1	4	yes	—
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×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
111	C₂²×Dic₁₉	—	2	1	no	—
112	C₂²×Dic₁₉	—	2	1	no	—
113	C₂²×Dic₁₉	—	2	1	no	—
114	C₂²×Dic₁₉	—	2	1	no	—
115	C₂²×Dic₁₉	—	2	2	no	—
116	C₂²×Dic₁₉	—	2	2	no	—
117	C₂²×Dic₁₉	—	2	2	no	—
118	C₂²×Dic₁₉	—	2	2	no	—
119	C₂²×Dic₁₉	—	2	2	no	—
120	C₂²×Dic₁₉	—	4	1	no	—
121	C₂²×Dic₁₉	—	4	1	no	—
122	C₂²×Dic₁₉	—	4	2	no	—
123	C₂²×Dic₁₉	—	4	2	no	—
124	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
128	M₁₆×C₁₉	—	2	2	no	—
129	M₁₆×C₁₉	—	2	2	no	—
130	M₁₆×C₁₉	—	2	2	no	—
131	M₁₆×C₁₉	—	2	2	no	—
132	M₁₆×C₁₉	—	4	1	no	—
133	M₁₆×C₁₉	—	4	1	no	—
134	M₁₆×C₁₉	—	4	1	no	—
135	M₁₆×C₁₉	—	4	1	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₂×C₈×C₁₉	—	4	1	no	—
139	C₂×C₈×C₁₉	—	4	1	no	—
140	C₂×C₈×C₁₉	—	4	1	no	—
141	C₂×C₈×C₁₉	—	4	1	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊Dic₁₉	—	4	4	no	—
147	C₄⋊Dic₁₉	—	4	1	no	—
148	C₄⋊Dic₁₉	—	4	1	no	—
149	C₄⋊Dic₁₉	—	4	1	no	—
150	C₄⋊Dic₁₉	—	4	1	no	—
151	C₄⋊Dic₁₉	—	4	4	no	—
152	C₄×Dic₁₉	—	2	1	no	—
153	C₄×Dic₁₉	—	2	1	no	—
154	C₄×Dic₁₉	—	2	1	no	—
155	C₄×Dic₁₉	—	2	1	no	—
156	C₄×Dic₁₉	—	2	1	no	—
157	C₄×Dic₁₉	—	2	1	no	—
158	C₄×Dic₁₉	—	2	1	no	—
159	C₄×Dic₁₉	—	2	1	no	—
160	#64520	—	2	2	no	—
161	#64520	—	2	2	no	—
162	#64520	—	2	2	no	—
163	#64520	—	2	2	no	—
164	#64520	—	4	1	no	—
165	#64520	—	4	1	no	—
166	#64520	—	4	1	no	—
167	#64520	—	4	1	no	—
168	C₂×C₁₉⋊C₈	—	2	2	no	—
169	C₂×C₁₉⋊C₈	—	2	2	no	—
170	C₂×C₁₉⋊C₈	—	4	1	no	—
171	C₂×C₁₉⋊C₈	—	4	1	no	—
172	C₂×C₁₉⋊C₈	—	4	1	no	—
173	C₂×C₁₉⋊C₈	—	4	1	no	—
174	#11204	—	19	1	no	maximal, Sylow
175	C₂³×C₁₉	—	2	1	no	—
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	2	1	no	—
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂³×C₁₉	#117	1	1	yes	characteristic
182	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
183	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
184	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
185	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	—	2	4	no	—
187	C₂×C₄×C₁₉	—	4	4	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
192	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
205	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
210	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
211	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
212	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
213	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
215	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
216	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
217	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
218	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
219	C₂×Dic₁₉	—	2	1	no	—
220	C₂×Dic₁₉	—	2	1	no	—
221	C₂×Dic₁₉	—	2	1	no	—
222	C₂×Dic₁₉	—	2	1	no	—
223	C₂×Dic₁₉	—	2	1	no	—
224	C₂×Dic₁₉	—	2	1	no	—
225	C₂×Dic₁₉	—	2	1	no	—
226	C₂×Dic₁₉	—	2	1	no	—
227	C₂×Dic₁₉	—	2	1	no	—
228	C₂×Dic₁₉	—	2	1	no	—
229	C₂×Dic₁₉	—	4	2	no	—
230	C₂×Dic₁₉	—	4	2	no	—
231	C₂×Dic₁₉	—	4	2	no	—
232	C₂×Dic₁₉	—	4	2	no	—
233	C₂×Dic₁₉	—	4	2	no	—
234	C₂×Dic₁₉	—	4	2	no	—
235	C₂×Dic₁₉	—	4	2	no	—
236	C₂×Dic₁₉	—	8	2	no	—
237	C₂×Dic₁₉	—	8	2	no	—
238	C₂×Dic₁₉	#100	1	2	yes	—
239	C₂×Dic₁₉	#101	1	2	yes	—
240	C₈×C₁₉	—	4	2	no	—
241	C₈×C₁₉	—	4	2	no	—
242	C₁₉⋊C₈	—	4	2	no	—
243	C₁₉⋊C₈	—	4	2	no	—
244	C₂×#423	—	19	1	no	—
245	C₂×#389	—	19	1	no	—
246	C₂×#343	—	19	1	no	—
247	C₂×#343	—	19	1	no	—
248	C₂×#343	—	19	1	no	—
249	C₂×#343	D₁₉	1	1	yes	characteristic
250	#1728	—	19	1	no	—
251	C₂²×C₁₉	—	2	1	no	—
252	C₂²×C₁₉	—	2	1	no	—
253	C₂²×C₁₉	—	2	1	no	—
254	C₂²×C₁₉	—	2	1	no	—
255	C₂²×C₁₉	—	2	1	no	—
256	C₂²×C₁₉	—	2	1	no	—
257	C₂²×C₁₉	—	2	1	no	—
258	C₂²×C₁₉	—	2	1	no	—
259	C₂²×C₁₉	—	2	1	no	—
260	C₂²×C₁₉	—	2	1	no	—
261	C₂²×C₁₉	—	2	1	no	—
262	C₂²×C₁₉	—	2	1	no	—
263	C₂²×C₁₉	#380	1	1	yes	characteristic
264	C₂²×C₁₉	#386	1	1	yes	characteristic
265	C₂²×C₁₉	#387	1	1	yes	characteristic
266	C₂²×C₁₉	#387	1	1	yes	characteristic
267	C₂²×C₁₉	#389	1	1	yes	characteristic
268	C₂²×C₁₉	#389	1	1	yes	characteristic
269	C₂²×C₁₉	#391	1	1	yes	characteristic
270	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
271	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
272	C₂²×C₁₉	#413	1	1	yes	characteristic
273	C₂²×C₁₉	#413	1	1	yes	characteristic
274	C₄×C₁₉	—	4	4	no	—
275	C₄×C₁₉	#394	1	1	yes	characteristic
276	C₄×C₁₉	#395	1	1	yes	characteristic
277	C₄×C₁₉	#396	1	1	yes	characteristic
278	C₄×C₁₉	#396	1	1	yes	characteristic
279	C₄×C₁₉	#398	1	1	yes	characteristic
280	C₄×C₁₉	#398	1	1	yes	characteristic
281	C₄×C₁₉	#398	1	1	yes	characteristic
282	C₄×C₁₉	#400	1	1	yes	characteristic
283	Dic₁₉	—	2	2	no	—
284	Dic₁₉	—	2	2	no	—
285	Dic₁₉	—	4	1	no	—
286	Dic₁₉	—	4	1	no	—
287	Dic₁₉	—	8	2	no	—
288	C₂²×M₁₆	—	19	1	no	—
289	C₂²×M₁₆	—	19	1	no	—
290	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
291	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
292	C₂²×C₄⋊C₄	—	19	1	no	—
293	C₂²×C₄⋊C₄	—	19	2	no	—
294	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
295	C₂²×C₄²	—	19	1	no	—
296	#423	—	38	2	no	—
297	#423	—	38	2	no	—
298	C₂×C₄⋊C₈	—	38	1	no	—
299	C₂×C₄⋊C₈	—	38	1	no	—
300	#389	—	38	1	no	—
301	#389	—	38	1	no	—
302	#389	—	38	1	no	—
303	#389	—	38	1	no	—
304	C₂×#95	—	19	2	no	—
305	#343	—	2	2	no	—
306	#343	—	38	2	no	—
307	#343	—	38	2	no	—
308	#343	—	38	2	no	—
309	#336	—	38	1	no	—
310	#336	—	38	1	no	—
311	C₂×C₁₉	—	2	1	no	—
312	C₂×C₁₉	—	2	1	no	—
313	C₂×C₁₉	—	2	1	no	—
314	C₂×C₁₉	—	2	1	no	—
315	C₂×C₁₉	#1441	1	1	yes	characteristic
316	C₂×C₁₉	#1800	1	1	yes	characteristic
317	C₂×C₁₉	#1801	1	1	yes	characteristic
318	C₂×C₁₉	#1900	1	1	yes	characteristic
319	C₂×C₁₉	#1901	1	1	yes	characteristic
320	C₂×C₁₉	#1997	1	1	yes	characteristic
321	C₂×C₁₉	#1998	1	1	yes	characteristic
322	C₂³×C₄	—	19	1	no	—
323	C₂³×C₄	—	19	1	no	—
324	C₂³×C₄	—	19	2	no	—
325	C₂³×C₄	C₄×D₁₉	1	2	yes	—
326	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	19	2	no	—
338	C₂×M₁₆	—	19	2	no	—
339	C₂×M₁₆	—	38	1	no	—
340	C₂×M₁₆	—	38	1	no	—
341	C₂×M₁₆	—	38	1	no	—
342	C₂×M₁₆	—	38	1	no	—
343	C₂×M₁₆	—	38	1	no	—
344	C₂×M₁₆	—	38	1	no	—
345	C₂×M₁₆	—	38	1	no	—
346	C₂×M₁₆	—	38	1	no	—
347	C₂×M₁₆	—	38	1	no	—
348	C₂×M₁₆	—	38	1	no	—
349	C₂×M₁₆	Dic₃₈	1	2	yes	—
350	C₂×M₁₆	D₇₆	1	2	yes	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	—	38	1	no	—
354	C₂²×C₈	—	38	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	38	2	no	—
360	C₂×C₄⋊C₄	—	38	2	no	—
361	C₂×C₄⋊C₄	—	38	1	no	—
362	C₂×C₄⋊C₄	—	38	1	no	—
363	C₂×C₄⋊C₄	—	38	1	no	—
364	C₂×C₄⋊C₄	—	38	1	no	—
365	C₂×C₄⋊C₄	—	38	1	no	—
366	C₂×C₄⋊C₄	—	38	1	no	—
367	C₂×C₄⋊C₄	—	76	4	no	—
368	C₂×C₄⋊C₄	Dic₃₈	1	2	yes	—
369	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
370	C₂×C₄²	—	19	1	no	—
371	C₂×C₄²	—	19	1	no	—
372	C₂×C₄²	—	19	1	no	—
373	C₂×C₄²	—	19	1	no	—
374	C₂×C₄²	—	38	1	no	—
375	C₂×C₄²	—	38	1	no	—
376	C₂×C₄²	—	38	1	no	—
377	C₂×C₄²	—	38	1	no	—
378	C₄⋊C₈	—	38	4	no	—
379	C₄⋊C₈	—	38	4	no	—
380	#95	—	38	2	no	—
381	#95	—	38	2	no	—
382	C₁₉	#11204	1	1	yes	characteristic, complemented, Sylow
383	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	19	1	no	—
389	C₂²×C₄	—	19	1	no	—
390	C₂²×C₄	—	19	1	no	—
391	C₂²×C₄	—	19	1	no	—
392	C₂²×C₄	—	38	2	no	—
393	C₂²×C₄	—	38	2	no	—
394	C₂²×C₄	—	38	1	no	—
395	C₂²×C₄	—	38	1	no	—
396	C₂²×C₄	—	38	1	no	—
397	C₂²×C₄	—	38	1	no	—
398	C₂²×C₄	—	38	2	no	—
399	C₂²×C₄	—	38	2	no	—
400	C₂²×C₄	—	38	2	no	—
401	C₂²×C₄	—	76	1	no	—
402	C₂²×C₄	—	76	1	no	—
403	C₂²×C₄	—	76	2	no	—
404	C₂²×C₄	—	76	2	no	—
405	C₂²×C₄	Dic₁₉⋊C₄	1	4	yes	—
406	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
407	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
409	C₂²×C₄	#64541	1	1	yes	characteristic
410	C₂²×C₄	#64541	1	1	yes	characteristic
411	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
412	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
413	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
414	C₂²×C₄	#64543	1	1	yes	characteristic
415	C₂²×C₄	#64543	1	1	yes	characteristic
416	C₂²×C₄	#64543	1	1	yes	characteristic
417	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
418	C₂²×C₄	#64545	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
420	M₁₆	—	2	2	no	—
421	M₁₆	—	2	2	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	2	no	—
424	M₁₆	—	4	1	no	—
425	M₁₆	—	4	1	no	—
426	M₁₆	—	4	1	no	—
427	M₁₆	—	4	1	no	—
428	M₁₆	—	38	2	no	—
429	M₁₆	—	38	2	no	—
430	M₁₆	—	38	2	no	—
431	M₁₆	—	38	2	no	—
432	M₁₆	—	76	1	no	—
433	M₁₆	—	76	1	no	—
434	M₁₆	—	76	1	no	—
435	M₁₆	—	76	1	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	4	1	no	—
439	C₂×C₈	—	4	1	no	—
440	C₂×C₈	—	4	1	no	—
441	C₂×C₈	—	4	1	no	—
442	C₂×C₈	—	38	2	no	—
443	C₂×C₈	—	38	2	no	—
444	C₂×C₈	—	76	1	no	—
445	C₂×C₈	—	76	1	no	—
446	C₂×C₈	—	76	1	no	—
447	C₂×C₈	—	76	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	76	4	no	—
453	C₄⋊C₄	—	76	4	no	—
454	C₄⋊C₄	—	76	1	no	—
455	C₄⋊C₄	—	76	1	no	—
456	C₄⋊C₄	—	76	1	no	—
457	C₄⋊C₄	—	76	1	no	—
458	C₄²	—	38	1	no	—
459	C₄²	—	38	1	no	—
460	C₄²	—	38	1	no	—
461	C₄²	—	38	1	no	—
462	C₄²	—	38	1	no	—
463	C₄²	—	38	1	no	—
464	C₄²	—	38	1	no	—
465	C₄²	—	38	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
471	C₂³	C₄×D₇₆	1	1	yes	characteristic
472	C₂³	#10597323	1	1	yes	characteristic
473	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
474	C₂³	#10597333	1	1	yes	characteristic
475	C₂³	#10597339	1	1	yes	characteristic
476	C₂³	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	19	2	no	—
483	C₂×C₄	—	19	2	no	—
484	C₂×C₄	—	38	1	no	—
485	C₂×C₄	—	38	1	no	—
486	C₂×C₄	—	38	1	no	—
487	C₂×C₄	—	38	1	no	—
488	C₂×C₄	—	38	1	no	—
489	C₂×C₄	—	38	1	no	—
490	C₂×C₄	—	38	1	no	—
491	C₂×C₄	—	38	1	no	—
492	C₂×C₄	—	38	1	no	—
493	C₂×C₄	—	38	1	no	—
494	C₂×C₄	—	76	2	no	—
495	C₂×C₄	—	76	2	no	—
496	C₂×C₄	—	76	2	no	—
497	C₂×C₄	—	76	2	no	—
498	C₂×C₄	—	76	2	no	—
499	C₂×C₄	—	76	2	no	—
500	C₂×C₄	—	76	2	no	—
501	C₂×C₄	—	152	2	no	—
502	C₂×C₄	—	152	2	no	—
503	C₂×C₄	#10597315	1	1	yes	characteristic
504	C₂×C₄	#10597316	1	1	yes	characteristic
505	C₂×C₄	#10597324	1	1	yes	characteristic
506	C₂×C₄	#10597324	1	1	yes	characteristic
507	C₂×C₄	#10597324	1	1	yes	characteristic
508	C₂×C₄	#10597324	1	1	yes	characteristic
509	C₂×C₄	#10597325	1	1	yes	characteristic
510	C₂×C₄	#10597328	1	1	yes	characteristic
511	C₂×C₄	#10597329	1	1	yes	characteristic
512	C₂×C₄	#10597330	1	1	yes	characteristic
513	C₂×C₄	#10597331	1	1	yes	characteristic
514	C₂×C₄	#10597332	1	1	yes	characteristic
515	C₂×C₄	#10597334	1	1	yes	characteristic
516	C₂×C₄	#10597334	1	1	yes	characteristic
517	C₂×C₄	#10597335	1	1	yes	characteristic
518	C₂×C₄	#10597336	1	1	yes	characteristic
519	C₂×C₄	#10597336	1	1	yes	characteristic
520	C₂×C₄	#10597340	1	1	yes	characteristic
521	C₂×C₄	#10597341	1	1	yes	characteristic
522	C₂×C₄	#10597342	1	1	yes	characteristic
523	C₂×C₄	#10597343	1	1	yes	characteristic
524	C₂×C₄	#10597344	1	1	yes	characteristic
525	C₂×C₄	#10597370	1	1	yes	characteristic
526	C₂×C₄	#10597376	1	1	yes	characteristic
527	C₂×C₄	#10597384	1	1	yes	characteristic
528	C₂×C₄	#10597385	1	1	yes	characteristic
529	C₂×C₄	#10597385	1	1	yes	characteristic
530	C₂×C₄	#10597392	1	1	yes	characteristic
531	C₈	—	4	2	no	—
532	C₈	—	4	2	no	—
533	C₈	—	76	2	no	—
534	C₈	—	76	2	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	#11926402	1	1	yes	characteristic
548	C₂²	#11926422	1	1	yes	characteristic
549	C₂²	#11926427	1	1	yes	characteristic
550	C₂²	#11926429	1	1	yes	characteristic
551	C₂²	#11926440	1	1	yes	characteristic
552	C₂²	#11926442	1	1	yes	characteristic
553	C₂²	#11926448	1	1	yes	characteristic
554	C₂²	#100×D₁₉	1	1	yes	characteristic
555	C₂²	#101×D₁₉	1	1	yes	characteristic
556	C₂²	#11926525	1	1	yes	characteristic
557	C₂²	#11926527	1	1	yes	characteristic
558	C₄	—	4	4	no	—
559	C₄	—	38	2	no	—
560	C₄	—	38	2	no	—
561	C₄	—	76	1	no	—
562	C₄	—	76	1	no	—
563	C₄	—	152	2	no	—
564	C₄	#11926460	1	1	yes	characteristic
565	C₄	#11926465	1	1	yes	characteristic
566	C₄	#11926466	1	1	yes	characteristic
567	C₄	#11926467	1	1	yes	characteristic
568	C₄	#11926476	1	1	yes	characteristic
569	C₄	#11926477	1	1	yes	characteristic
570	C₄	#11926478	1	1	yes	characteristic
571	C₄	#11926486	1	1	yes	characteristic
572	C₂	—	2	1	no	—
573	C₂	—	2	1	no	—
574	C₂	—	2	1	no	—
575	C₂	—	2	1	no	—
576	C₂	#14561887	1	1	yes	characteristic
577	C₂	#14563625	1	1	yes	characteristic
578	C₂	#14563629	1	1	yes	characteristic
579	C₂	#14564097	1	1	yes	characteristic
580	C₂	#14564102	1	1	yes	characteristic
581	C₂	#14564622	1	1	yes	characteristic
582	C₂	#14564626	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#343	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#343	D₁₉
hypocenter	C₁₉	#11204
LCS	G ▷ C₂⁴×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
382. C₁₉	#11204	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926567	2
C₂×#11926443	2
C₂×#11926313	2
C₂×#11926312	2
#14563328	2
C₂×C₁₉×#343	2
#11204	19