Subgroups — #18088005

Order 4864.

1298 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926561	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926316	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563368	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926305	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11926303	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2896	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	#41×Dic₁₉	—	2	2	no	—
10	#41×Dic₁₉	—	2	2	no	—
11	#41×Dic₁₉	—	2	2	no	—
12	#41×Dic₁₉	C₄	1	4	yes	complemented
13	C₂×Q₈×Dic₁₉	—	2	1	no	—
14	C₂×D₄×Dic₁₉	—	2	1	no	—
15	C₂×D₄×Dic₁₉	—	2	2	no	—
16	C₂×#10597372	—	2	1	no	—
17	C₂×#10597372	C₂²	1	1	yes	characteristic
18	C₂×#10597372	C₂²	1	1	yes	characteristic
19	C₂²×C₄×Dic₁₉	—	2	1	no	—
20	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
21	#11926561	—	2	2	no	—
22	#11926561	C₄	1	4	yes	complemented
23	C₂×#10597294	—	2	2	no	—
24	#11926316	—	2	2	no	—
25	#11926311	—	2	2	no	—
26	#11926305	—	2	2	no	—
27	#11926303	—	2	1	no	—
28	#11926303	—	2	1	no	—
29	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
32	C₁₉×#419	—	2	1	no	—
33	C₁₉×#418	—	2	1	no	—
34	C₁₉×#417	C₄	1	4	yes	complemented
35	C₁₉×#416	—	2	2	no	—
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
44	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×#41×C₁₉	D₄	1	2	yes	—
46	C₂×#41×C₁₉	D₄	1	2	yes	—
47	C₂×#41×C₁₉	Q₈	1	2	yes	—
48	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
53	C₂³×Dic₁₉	—	2	2	no	—
54	C₂³×Dic₁₉	—	2	1	no	—
55	C₂×M₁₆×C₁₉	—	2	1	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	1	no	—
58	C₂×M₁₆×C₁₉	—	2	1	no	—
59	C₂×M₁₆×C₁₉	—	2	1	no	—
60	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	complemented
61	C₂²×C₈×C₁₉	—	2	1	no	—
62	C₁₉×#117	—	2	1	no	—
63	C₁₉×#117	—	2	1	no	—
64	C₁₉×#117	—	2	1	no	—
65	C₁₉×#117	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	complemented
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₄²×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
70	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
71	C₂×C₂²⋊Dic₁₉	D₄	1	2	yes	—
72	Q₈×Dic₁₉	—	2	4	no	—
73	Q₈×Dic₁₉	—	2	4	no	—
74	D₄×Dic₁₉	—	2	8	no	—
75	D₄×Dic₁₉	—	2	4	no	—
76	D₄×Dic₁₉	—	2	4	no	—
77	D₄×Dic₁₉	—	2	8	no	—
78	#10597372	—	2	4	no	—
79	#10597372	—	2	1	no	—
80	#10597372	—	2	1	no	—
81	#10597372	—	2	1	no	—
82	#10597372	—	2	4	no	—
83	#10597372	—	2	1	no	—
84	#10597372	—	2	1	no	—
85	#10597372	C₂×C₄	1	2	yes	—
86	#10597372	C₂×C₄	1	2	yes	complemented
87	#10597372	D₄	1	2	yes	—
88	C₂×C₄⋊Dic₁₉	—	2	2	no	—
89	C₂×C₄⋊Dic₁₉	—	2	1	no	—
90	C₂×C₄⋊Dic₁₉	—	2	1	no	—
91	C₂×C₄×Dic₁₉	—	2	2	no	—
92	C₂×C₄×Dic₁₉	—	2	4	no	—
93	C₂×C₄×Dic₁₉	—	2	1	no	—
94	C₂×C₄×Dic₁₉	—	2	1	no	—
95	C₂×C₄×Dic₁₉	—	2	1	no	—
96	C₂×C₄×Dic₁₉	—	2	1	no	—
97	C₂×C₄×Dic₁₉	—	2	4	no	—
98	C₂×C₄×Dic₁₉	—	2	1	no	—
99	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
100	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
101	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
102	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
103	C₂×#64520	—	2	1	no	—
104	C₂×#64520	—	2	1	no	—
105	C₂×#64520	—	2	1	no	—
106	C₂×#64520	—	2	1	no	—
107	C₂×#64520	—	2	1	no	—
108	C₂×#64520	C₂×C₄	1	2	yes	complemented
109	C₂²×C₁₉⋊C₈	—	2	1	no	—
110	C₁₉×#103	—	2	4	no	—
111	C₁₉×#102	—	2	4	no	—
112	#10597294	—	2	8	no	—
113	C₂⁴×C₁₉	—	2	1	no	—
114	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
115	#41×C₁₉	—	2	2	no	—
116	#41×C₁₉	—	2	2	no	—
117	#41×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	2	2	no	—
127	#41×C₁₉	C₄²	1	4	yes	—
128	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
129	#41×C₁₉	C₄⋊C₄	1	4	yes	—
130	#41×C₁₉	C₄⋊C₄	1	4	yes	—
131	C₂×Q₈×C₁₉	—	2	1	no	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
135	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
136	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
137	C₂×D₄×C₁₉	—	2	2	no	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	1	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
147	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
148	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
149	C₂²×C₄×C₁₉	—	2	1	no	—
150	C₂²×C₄×C₁₉	—	2	2	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
167	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
171	C₂²×Dic₁₉	—	2	1	no	—
172	C₂²×Dic₁₉	—	2	8	no	—
173	C₂²×Dic₁₉	—	2	2	no	—
174	C₂²×Dic₁₉	—	2	2	no	—
175	C₂²×Dic₁₉	—	2	1	no	—
176	C₂²×Dic₁₉	—	2	2	no	—
177	C₂²×Dic₁₉	—	4	4	no	—
178	C₂²×Dic₁₉	—	4	8	no	—
179	C₂²×Dic₁₉	—	4	1	no	—
180	M₁₆×C₁₉	—	2	2	no	—
181	M₁₆×C₁₉	—	2	2	no	—
182	M₁₆×C₁₉	—	4	1	no	—
183	M₁₆×C₁₉	—	4	1	no	—
184	C₂×C₈×C₁₉	—	2	2	no	—
185	C₂×C₈×C₁₉	—	4	1	no	—
186	C₂×C₈×C₁₉	—	4	1	no	—
187	C₄⋊C₄×C₁₉	—	2	2	no	—
188	C₄⋊C₄×C₁₉	—	2	2	no	—
189	C₂²⋊C₄×C₁₉	—	4	1	no	—
190	C₂²⋊C₄×C₁₉	—	4	1	no	—
191	C₄²×C₁₉	—	4	1	no	—
192	C₄²×C₁₉	—	4	1	no	—
193	C₂²⋊Dic₁₉	—	2	8	no	—
194	C₂²⋊Dic₁₉	—	2	2	no	—
195	C₂²⋊Dic₁₉	—	2	2	no	—
196	C₂²⋊Dic₁₉	—	4	1	no	—
197	C₂²⋊Dic₁₉	C₂²⋊C₄	1	4	yes	—
198	C₄⋊Dic₁₉	—	2	8	no	—
199	C₄⋊Dic₁₉	—	2	2	no	—
200	C₄⋊Dic₁₉	—	2	2	no	—
201	C₄⋊Dic₁₉	—	2	2	no	—
202	C₄⋊Dic₁₉	—	4	1	no	—
203	C₄×Dic₁₉	—	2	8	no	—
204	C₄×Dic₁₉	—	2	2	no	—
205	C₄×Dic₁₉	—	2	2	no	—
206	C₄×Dic₁₉	—	2	2	no	—
207	C₄×Dic₁₉	—	2	1	no	—
208	C₄×Dic₁₉	—	2	2	no	—
209	C₄×Dic₁₉	—	2	1	no	—
210	C₄×Dic₁₉	—	2	2	no	—
211	C₄×Dic₁₉	—	4	1	no	—
212	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
213	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
214	#64520	—	2	2	no	—
215	#64520	—	2	2	no	—
216	#64520	—	4	1	no	—
217	#64520	—	4	1	no	—
218	C₂×C₁₉⋊C₈	—	2	2	no	—
219	C₂×C₁₉⋊C₈	—	4	1	no	—
220	C₂×C₁₉⋊C₈	—	4	1	no	—
221	#10772	—	19	1	no	maximal, Sylow
222	C₂³×C₁₉	—	2	2	no	—
223	C₂³×C₁₉	—	2	2	no	—
224	C₂³×C₁₉	—	2	2	no	—
225	C₂³×C₁₉	—	4	2	no	—
226	C₂³×C₁₉	—	4	4	no	—
227	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
229	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
230	C₂³×C₁₉	#120	1	1	yes	characteristic
231	C₂³×C₁₉	#120	1	1	yes	characteristic
232	C₂³×C₁₉	#121	1	1	yes	characteristic
233	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
234	Q₈×C₁₉	—	2	2	no	—
235	Q₈×C₁₉	—	2	2	no	—
236	Q₈×C₁₉	—	2	2	no	—
237	Q₈×C₁₉	#95	1	4	yes	—
238	D₄×C₁₉	—	2	4	no	—
239	D₄×C₁₉	—	2	4	no	—
240	D₄×C₁₉	—	2	4	no	—
241	D₄×C₁₉	—	2	4	no	—
242	D₄×C₁₉	—	2	2	no	—
243	D₄×C₁₉	—	2	2	no	—
244	D₄×C₁₉	—	2	2	no	—
245	D₄×C₁₉	#95	1	4	yes	—
246	C₂×C₄×C₁₉	—	2	2	no	—
247	C₂×C₄×C₁₉	—	2	2	no	—
248	C₂×C₄×C₁₉	—	2	2	no	—
249	C₂×C₄×C₁₉	—	2	4	no	—
250	C₂×C₄×C₁₉	—	2	4	no	—
251	C₂×C₄×C₁₉	—	2	4	no	—
252	C₂×C₄×C₁₉	—	2	4	no	—
253	C₂×C₄×C₁₉	—	4	2	no	—
254	C₂×C₄×C₁₉	—	8	2	no	—
255	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
256	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
264	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
265	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
271	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
273	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
274	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
275	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
276	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
277	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
278	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
279	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
280	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
281	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
282	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
283	C₂×Dic₁₉	—	2	4	no	—
284	C₂×Dic₁₉	—	2	2	no	—
285	C₂×Dic₁₉	—	2	4	no	—
286	C₂×Dic₁₉	—	2	2	no	—
287	C₂×Dic₁₉	—	4	4	no	—
288	C₂×Dic₁₉	—	4	4	no	—
289	C₂×Dic₁₉	—	4	16	no	—
290	C₂×Dic₁₉	—	4	2	no	—
291	C₂×Dic₁₉	—	4	4	no	—
292	C₂×Dic₁₉	—	4	2	no	—
293	C₂×Dic₁₉	—	8	2	no	—
294	C₈×C₁₉	—	4	2	no	—
295	C₁₉⋊C₈	—	4	2	no	—
296	C₂×C₄×#41	—	19	1	no	—
297	C₂×#421	—	19	1	no	—
298	#2896	D₁₉	1	1	yes	characteristic
299	C₂×#344	—	19	1	no	—
300	#1740	—	19	1	no	—
301	C₂×#339	—	19	1	no	—
302	C₂×#339	—	19	1	no	—
303	C₂²×C₁₉	—	2	2	no	—
304	C₂²×C₁₉	—	2	2	no	—
305	C₂²×C₁₉	—	2	2	no	—
306	C₂²×C₁₉	—	2	4	no	—
307	C₂²×C₁₉	—	4	1	no	—
308	C₂²×C₁₉	—	4	1	no	—
309	C₂²×C₁₉	—	4	1	no	—
310	C₂²×C₁₉	—	4	1	no	—
311	C₂²×C₁₉	—	4	4	no	—
312	C₂²×C₁₉	—	4	4	no	—
313	C₂²×C₁₉	—	4	4	no	—
314	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₁₉	#379	1	1	yes	characteristic
316	C₂²×C₁₉	#380	1	1	yes	characteristic
317	C₂²×C₁₉	#385	1	1	yes	characteristic
318	C₂²×C₁₉	#385	1	1	yes	characteristic
319	C₂²×C₁₉	#386	1	1	yes	characteristic
320	C₂²×C₁₉	#386	1	1	yes	characteristic
321	C₄×C₁₉	—	2	4	no	—
322	C₄×C₁₉	—	8	2	no	—
323	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
324	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
325	C₄×C₁₉	#380	1	1	yes	characteristic
326	C₄×C₁₉	#381	1	1	yes	characteristic
327	C₄×C₁₉	#385	1	1	yes	characteristic
328	C₄×C₁₉	#385	1	1	yes	characteristic
329	C₄×C₁₉	#386	1	1	yes	characteristic
330	C₄×C₁₉	#386	1	1	yes	characteristic
331	Dic₁₉	—	2	4	no	—
332	Dic₁₉	—	4	4	no	—
333	Dic₁₉	—	4	2	no	—
334	Dic₁₉	—	8	2	no	—
335	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
336	C₂²×M₁₆	—	19	1	no	—
337	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
338	C₄×#41	—	19	4	no	—
339	C₄×#41	—	38	2	no	—
340	C₄×#41	—	38	2	no	—
341	C₄×#41	—	38	2	no	—
342	C₂×C₄×Q₈	—	38	1	no	—
343	C₂×C₄×D₄	—	38	2	no	—
344	C₂×C₄×D₄	—	38	1	no	—
345	C₂×#117	—	19	1	no	—
346	C₂×#117	—	19	1	no	—
347	C₂×#117	—	38	1	no	—
348	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
349	C₂²×C₄²	—	19	1	no	—
350	C₂²×C₄²	—	38	1	no	—
351	#421	—	19	4	no	—
352	#421	—	38	2	no	—
353	C₂×#104	—	38	2	no	—
354	#419	—	2	1	no	—
355	#418	—	2	1	no	—
356	#417	Dic₁₉	1	4	yes	complemented
357	#416	—	2	2	no	—
358	#344	—	38	2	no	—
359	#342	—	38	2	no	—
360	#339	—	38	1	no	—
361	#339	—	38	1	no	—
362	#339	—	38	2	no	—
363	C₂×C₁₉	—	2	1	no	—
364	C₂×C₁₉	—	2	1	no	—
365	C₂×C₁₉	—	2	1	no	—
366	C₂×C₁₉	—	2	1	no	—
367	C₂×C₁₉	—	2	1	no	—
368	C₂×C₁₉	—	2	1	no	—
369	C₂×C₁₉	—	4	4	no	—
370	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
371	C₂×C₁₉	#1906	1	2	yes	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	1	no	—
376	C₂×#41	—	2	1	no	—
377	C₂×#41	—	2	1	no	—
378	C₂×#41	Dic₃₈	1	2	yes	—
379	C₂×#41	C₄×D₁₉	1	2	yes	—
380	C₂×#41	C₄×D₁₉	1	2	yes	—
381	C₂×#41	D₇₆	1	2	yes	—
382	C₂×#41	C₂×Dic₁₉	1	2	yes	—
383	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
384	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
385	C₂²×D₄	—	2	1	no	—
386	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	38	2	no	—
389	C₂³×C₄	—	38	1	no	—
390	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	no	—
396	C₂×M₁₆	—	19	2	no	—
397	C₂×M₁₆	—	38	1	no	—
398	C₂×M₁₆	—	38	1	no	—
399	C₂×M₁₆	—	38	1	no	—
400	C₂×M₁₆	—	38	1	no	—
401	C₂×M₁₆	—	38	1	no	—
402	C₂×M₁₆	C₂×Dic₁₉	1	2	yes	complemented
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	38	1	no	—
405	C₄×Q₈	—	38	4	no	—
406	C₄×Q₈	—	38	4	no	—
407	C₄×D₄	—	38	8	no	—
408	C₄×D₄	—	38	8	no	—
409	C₄×D₄	—	38	4	no	—
410	C₄×D₄	—	38	4	no	—
411	#117	—	2	1	no	—
412	#117	—	2	1	no	—
413	#117	—	2	1	no	—
414	#117	—	2	1	no	—
415	#117	—	19	2	no	—
416	#117	—	19	2	no	—
417	#117	—	19	2	no	—
418	#117	—	38	4	no	—
419	#117	—	38	4	no	—
420	#117	—	38	1	no	—
421	#117	—	38	1	no	—
422	#117	—	38	1	no	—
423	#117	—	38	1	no	—
424	#117	—	38	1	no	—
425	C₂×C₄⋊C₄	—	38	2	no	—
426	C₂×C₄⋊C₄	—	38	1	no	—
427	C₂×C₄⋊C₄	—	38	1	no	—
428	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	complemented
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	19	2	no	—
431	C₂×C₂²⋊C₄	—	38	2	no	—
432	C₂×C₂²⋊C₄	—	38	1	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	—	19	2	no	—
435	C₂×C₄²	—	19	1	no	—
436	C₂×C₄²	—	19	2	no	—
437	C₂×C₄²	—	19	1	no	—
438	C₂×C₄²	—	38	4	no	—
439	C₂×C₄²	—	38	2	no	—
440	C₂×C₄²	—	38	4	no	—
441	C₂×C₄²	—	38	1	no	—
442	C₂×C₄²	—	38	1	no	—
443	C₂×C₄²	—	38	1	no	—
444	C₂×C₄²	—	38	1	no	—
445	C₂×C₄²	—	38	1	no	—
446	#104	—	38	8	no	—
447	#103	—	2	4	no	—
448	#102	—	2	4	no	—
449	C₁₉	#10772	1	1	yes	characteristic, complemented, Sylow
450	C₂⁴	—	2	1	no	—
451	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
452	#41	—	2	2	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	2	2	no	—
460	#41	—	2	2	no	—
461	#41	—	2	2	no	—
462	#41	—	2	2	no	—
463	#41	—	2	2	no	—
464	#41	C₄×Dic₁₉	1	4	yes	—
465	#41	Dic₁₉⋊C₄	1	4	yes	—
466	#41	C₄⋊Dic₁₉	1	4	yes	—
467	#41	(C₂×D₁₉)⋊C₄	1	4	yes	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
472	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
473	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
484	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
485	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	38	1	no	—
495	C₂²×C₄	—	38	8	no	—
496	C₂²×C₄	—	38	1	no	—
497	C₂²×C₄	—	38	2	no	—
498	C₂²×C₄	—	38	2	no	—
499	C₂²×C₄	—	38	2	no	—
500	C₂²×C₄	—	76	4	no	—
501	C₂²×C₄	—	76	8	no	—
502	C₂²×C₄	—	76	1	no	—
503	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
507	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
508	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
509	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
510	C₂²×C₄	#64543	1	1	yes	characteristic
511	C₂²×C₄	#64543	1	1	yes	characteristic
512	C₂²×C₄	#64543	1	1	yes	characteristic
513	C₂²×C₄	#64543	1	1	yes	characteristic
514	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
515	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
517	M₁₆	—	2	2	no	—
518	M₁₆	—	2	2	no	—
519	M₁₆	—	4	1	no	—
520	M₁₆	—	4	1	no	—
521	M₁₆	—	38	2	no	—
522	M₁₆	—	38	2	no	—
523	M₁₆	—	76	1	no	—
524	M₁₆	—	76	1	no	—
525	C₂×C₈	—	2	2	no	—
526	C₂×C₈	—	4	1	no	—
527	C₂×C₈	—	4	1	no	—
528	C₂×C₈	—	38	2	no	—
529	C₂×C₈	—	76	1	no	—
530	C₂×C₈	—	76	1	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	2	2	no	—
533	C₄⋊C₄	—	38	8	no	—
534	C₄⋊C₄	—	38	2	no	—
535	C₄⋊C₄	—	38	2	no	—
536	C₄⋊C₄	—	38	2	no	—
537	C₄⋊C₄	—	76	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₂²⋊C₄	—	19	4	no	—
541	C₂²⋊C₄	—	38	8	no	—
542	C₂²⋊C₄	—	38	2	no	—
543	C₂²⋊C₄	—	38	2	no	—
544	C₂²⋊C₄	—	76	1	no	—
545	C₄²	—	4	1	no	—
546	C₄²	—	4	1	no	—
547	C₄²	—	19	2	no	—
548	C₄²	—	19	2	no	—
549	C₄²	—	38	8	no	—
550	C₄²	—	38	2	no	—
551	C₄²	—	38	2	no	—
552	C₄²	—	38	1	no	—
553	C₄²	—	38	1	no	—
554	C₄²	—	38	2	no	—
555	C₄²	—	38	2	no	—
556	C₄²	—	38	2	no	—
557	C₄²	—	76	1	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	4	no	—
563	C₂³	#10597324	1	1	yes	characteristic
564	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
565	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
566	C₂³	#10597328	1	1	yes	characteristic
567	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
568	C₂³	#10597383	1	1	yes	characteristic
569	C₂³	#10597385	1	1	yes	characteristic
570	Q₈	—	2	2	no	—
571	Q₈	—	2	2	no	—
572	Q₈	—	2	2	no	—
573	Q₈	C₁₉⋊#95	1	4	yes	—
574	D₄	—	2	4	no	—
575	D₄	—	2	4	no	—
576	D₄	—	2	4	no	—
577	D₄	—	2	4	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	C₁₉⋊#95	1	4	yes	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	8	2	no	—
591	C₂×C₄	—	38	4	no	—
592	C₂×C₄	—	38	2	no	—
593	C₂×C₄	—	38	2	no	—
594	C₂×C₄	—	38	4	no	—
595	C₂×C₄	—	76	4	no	—
596	C₂×C₄	—	76	4	no	—
597	C₂×C₄	—	76	16	no	—
598	C₂×C₄	—	76	2	no	—
599	C₂×C₄	—	76	4	no	—
600	C₂×C₄	—	76	2	no	—
601	C₂×C₄	—	152	2	no	—
602	C₂×C₄	#10597323	1	1	yes	characteristic
603	C₂×C₄	#10597323	1	1	yes	characteristic
604	C₂×C₄	#10597324	1	1	yes	characteristic
605	C₂×C₄	#10597324	1	1	yes	characteristic
606	C₂×C₄	#10597324	1	1	yes	characteristic
607	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
608	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
609	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
610	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
611	C₂×C₄	#10597328	1	1	yes	characteristic
612	C₂×C₄	#10597332	1	1	yes	characteristic
613	C₂×C₄	#10597332	1	1	yes	characteristic
614	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
615	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
616	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
617	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
618	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
619	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
620	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
621	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
622	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
623	C₂×C₄	#10597381	1	1	yes	characteristic
624	C₂×C₄	#10597381	1	1	yes	characteristic
625	C₂×C₄	#10597383	1	1	yes	characteristic
626	C₂×C₄	#10597385	1	1	yes	characteristic
627	C₂×C₄	#10597385	1	1	yes	characteristic
628	C₂×C₄	#10597385	1	1	yes	characteristic
629	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
630	C₈	—	4	2	no	—
631	C₈	—	76	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	4	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
644	C₂²	#11926399	1	1	yes	characteristic
645	C₂²	#11926402	1	1	yes	characteristic
646	C₂²	#11926416	1	1	yes	characteristic
647	C₂²	#11926419	1	1	yes	characteristic
648	C₂²	#11926421	1	1	yes	characteristic
649	C₂²	#11926424	1	1	yes	characteristic
650	C₄	—	2	4	no	—
651	C₄	—	8	2	no	—
652	C₄	—	38	4	no	—
653	C₄	—	76	2	no	—
654	C₄	—	76	4	no	—
655	C₄	—	152	2	no	—
656	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
657	C₄	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
658	C₄	#11926402	1	1	yes	characteristic
659	C₄	#11926405	1	1	yes	characteristic
660	C₄	#11926416	1	1	yes	characteristic
661	C₄	#11926419	1	1	yes	characteristic
662	C₄	#11926421	1	1	yes	characteristic
663	C₄	#11926424	1	1	yes	characteristic
664	C₂	—	2	1	no	—
665	C₂	—	2	1	no	—
666	C₂	—	2	1	no	—
667	C₂	—	2	1	no	—
668	C₂	—	2	1	no	—
669	C₂	—	2	1	no	—
670	C₂	—	4	4	no	—
671	C₂	#14561857	1	1	yes	characteristic
672	C₂	#14564138	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597385
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#2896	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#2896	D₁₉
hypocenter	C₁₉	#10772
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2896

Complements

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

N	H ≅ G/N	type
3. C₂×#11926316	C₂	semidirect
4. #14563368	C₂	semidirect
5. C₂×#11926305	C₂	semidirect
6. C₂×#11926303	C₂	semidirect
12. #41×Dic₁₉	C₄	semidirect
22. #11926561	C₄	semidirect
34. C₁₉×#417	C₄	semidirect
60. C₂×M₁₆×C₁₉	C₂×C₄	semidirect
66. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
86. #10597372	C₂×C₄	semidirect
108. C₂×#64520	C₂×C₄	semidirect
356. #417	Dic₁₉	semidirect
402. C₂×M₁₆	C₂×Dic₁₉	semidirect
428. C₂×C₄⋊C₄	C₂×Dic₁₉	semidirect
449. C₁₉	#10772	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×Dic₁₉	2
C₂×#11926561	2
C₂×#11926316	2
#14563368	2
C₂×#11926305	2
C₂×#11926303	2
C₁₉×#2896	2
#10772	19