Subgroups — #18088414

Order 4864.

918 conjugacy classes of subgroups.

The subgroup lattice has 512 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×M₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926413	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926313	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926312	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	C₂²	1	1	yes	characteristic
11	C₂²×Dic₁₉⋊C₄	C₄	1	4	yes	—
12	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
13	#11926567	—	2	2	no	—
14	#11926567	C₄	1	4	yes	complemented
15	C₂×Dic₁₉⋊C₈	—	2	2	no	—
16	M₁₆×Dic₁₉	—	2	2	no	—
17	M₁₆×Dic₁₉	C₄	1	4	yes	complemented
18	C₂×#10597272	—	2	1	no	—
19	C₂×C₈×Dic₁₉	—	2	1	no	—
20	#11926413	—	2	2	no	—
21	#11926413	—	2	1	no	—
22	#11926413	—	2	1	no	—
23	#11926313	—	2	2	no	—
24	#11926312	—	2	2	no	—
25	#11926312	—	2	2	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	—	2	2	no	—
30	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
33	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
40	C₂×M₁₆×C₁₉	—	2	1	no	—
41	C₂×M₁₆×C₁₉	—	2	1	no	—
42	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
44	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
45	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
46	C₂²×C₈×C₁₉	—	2	1	no	—
47	C₂²×C₈×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	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂×C₄⋊Dic₁₉	—	2	1	no	—
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×Dic₁₉⋊C₄	—	2	4	no	—
61	C₂×Dic₁₉⋊C₄	—	2	4	no	—
62	C₂×Dic₁₉⋊C₄	—	4	8	no	—
63	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
66	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
67	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
68	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
69	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
70	C₂×#64520	—	2	1	no	—
71	C₂×#64520	—	2	1	no	—
72	C₂×#64520	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
79	C₂×#64520	C₂×C₄	1	2	yes	—
80	C₂×#64520	D₄	1	2	yes	—
81	C₂×#64520	Q₈	1	2	yes	—
82	C₂²×C₁₉⋊C₈	—	2	1	no	—
83	C₂²×C₁₉⋊C₈	—	2	1	no	—
84	#10597272	—	2	4	no	—
85	Dic₁₉⋊C₈	—	2	8	no	—
86	C₈×Dic₁₉	—	2	4	no	—
87	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	4	4	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	C₂×D₄	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	C₂×Q₈	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	4	no	—
107	C₂²×Dic₁₉	—	2	4	no	—
108	C₂²×Dic₁₉	—	2	2	no	—
109	C₂²×Dic₁₉	—	2	2	no	—
110	C₂²×Dic₁₉	—	2	2	no	—
111	C₂²×Dic₁₉	—	4	4	no	—
112	C₂²×Dic₁₉	C₄²	1	4	yes	—
113	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
114	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
115	C₂²×Dic₁₉	C₄⋊C₄	1	4	yes	—
116	M₁₆×C₁₉	—	2	2	no	—
117	M₁₆×C₁₉	—	2	2	no	—
118	M₁₆×C₁₉	—	2	2	no	—
119	M₁₆×C₁₉	—	2	2	no	—
120	M₁₆×C₁₉	—	2	2	no	—
121	M₁₆×C₁₉	—	4	1	no	—
122	M₁₆×C₁₉	—	4	1	no	—
123	M₁₆×C₁₉	C₄⋊C₄	1	4	yes	complemented
124	C₂×C₈×C₁₉	—	2	2	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	2	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	4	1	no	—
129	C₂×C₈×C₁₉	—	4	1	no	—
130	C₄⋊C₄×C₁₉	—	4	1	no	—
131	C₄⋊C₄×C₁₉	—	4	1	no	—
132	C₄⋊C₄×C₁₉	—	4	1	no	—
133	C₄⋊C₄×C₁₉	—	4	1	no	—
134	C₄⋊Dic₁₉	—	4	1	no	—
135	C₄⋊Dic₁₉	—	4	1	no	—
136	C₄⋊Dic₁₉	—	4	1	no	—
137	C₄⋊Dic₁₉	—	4	1	no	—
138	Dic₁₉⋊C₄	—	4	8	no	—
139	Dic₁₉⋊C₄	—	4	8	no	—
140	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
141	C₄×Dic₁₉	C₂²⋊C₄	1	4	yes	—
142	C₄×Dic₁₉	C₂²⋊C₄	1	2	yes	—
143	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
144	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	—
145	C₄×Dic₁₉	C₄⋊C₄	1	2	yes	—
146	#64520	—	2	2	no	—
147	#64520	—	2	2	no	—
148	#64520	—	2	2	no	—
149	#64520	—	2	2	no	—
150	#64520	—	2	2	no	—
151	#64520	—	4	1	no	—
152	#64520	—	4	1	no	—
153	#64520	C₄⋊C₄	1	4	yes	complemented
154	C₂×C₁₉⋊C₈	—	2	2	no	—
155	C₂×C₁₉⋊C₈	—	2	2	no	—
156	C₂×C₁₉⋊C₈	—	2	2	no	—
157	C₂×C₁₉⋊C₈	—	2	2	no	—
158	C₂×C₁₉⋊C₈	—	4	1	no	—
159	C₂×C₁₉⋊C₈	—	4	1	no	—
160	#10857	—	19	1	no	maximal, Sylow
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	C₂×C₄²	1	1	yes	characteristic
164	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
167	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
169	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₉	—	4	2	no	—
171	C₂×C₄×C₁₉	—	4	4	no	—
172	C₂×C₄×C₁₉	—	8	2	no	—
173	C₂×C₄×C₁₉	—	8	2	no	—
174	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
190	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
196	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
197	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
198	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
199	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
202	C₂×Dic₁₉	—	2	2	no	—
203	C₂×Dic₁₉	—	2	2	no	—
204	C₂×Dic₁₉	—	2	8	no	—
205	C₂×Dic₁₉	—	2	8	no	—
206	C₂×Dic₁₉	—	4	2	no	—
207	C₂×Dic₁₉	—	4	4	no	—
208	C₂×Dic₁₉	—	8	2	no	—
209	C₂×Dic₁₉	—	8	2	no	—
210	C₂×Dic₁₉	#95	1	4	yes	—
211	C₂×Dic₁₉	#95	1	4	yes	—
212	C₂×Dic₁₉	#100	1	4	yes	—
213	C₂×Dic₁₉	#101	1	4	yes	—
214	C₈×C₁₉	—	2	4	no	—
215	C₈×C₁₉	—	4	2	no	—
216	C₁₉⋊C₈	—	2	4	no	—
217	C₁₉⋊C₈	—	4	2	no	—
218	C₂×#423	—	19	1	no	—
219	C₂×C₄×M₁₆	—	19	1	no	—
220	C₂×#384	—	19	1	no	—
221	C₂×#343	—	19	1	no	—
222	C₂×#343	—	19	1	no	—
223	C₂×#343	—	19	1	no	—
224	C₂×#343	D₁₉	1	1	yes	characteristic
225	C₂²×C₁₉	—	2	1	no	—
226	C₂²×C₁₉	—	2	1	no	—
227	C₂²×C₁₉	—	2	1	no	—
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	2	no	—
230	C₂²×C₁₉	—	2	2	no	—
231	C₂²×C₁₉	—	2	2	no	—
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	C₂×#95	1	1	yes	characteristic
234	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
235	C₂²×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
236	C₂²×C₁₉	#389	1	1	yes	characteristic
237	C₂²×C₁₉	#389	1	1	yes	characteristic
238	C₂²×C₁₉	#390	1	1	yes	characteristic
239	C₂²×C₁₉	#391	1	1	yes	characteristic
240	C₂²×C₁₉	C₂×#100	1	2	yes	—
241	C₂²×C₁₉	C₂×#101	1	2	yes	—
242	C₄×C₁₉	—	8	2	no	—
243	C₄×C₁₉	#380	1	1	yes	characteristic
244	C₄×C₁₉	#380	1	1	yes	characteristic
245	C₄×C₁₉	#382	1	1	yes	characteristic
246	C₄×C₁₉	#384	1	1	yes	characteristic
247	C₄×C₁₉	#389	1	1	yes	characteristic
248	C₄×C₁₉	#389	1	1	yes	characteristic
249	C₄×C₁₉	#390	1	1	yes	characteristic
250	C₄×C₁₉	#391	1	1	yes	characteristic
251	Dic₁₉	—	2	4	no	—
252	Dic₁₉	—	8	2	no	—
253	Dic₁₉	#343	1	8	yes	complemented
254	C₂²×M₁₆	—	19	1	no	—
255	C₂²×M₁₆	—	19	1	no	—
256	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
257	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
258	C₂²×C₄⋊C₄	—	19	1	no	—
259	C₂²×C₄⋊C₄	—	19	4	no	—
260	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
261	C₂²×C₄²	—	19	1	no	—
262	#423	—	19	4	no	—
263	#423	—	38	2	no	—
264	C₂×C₄⋊C₈	—	38	2	no	—
265	C₄×M₁₆	—	19	4	no	—
266	C₄×M₁₆	—	38	2	no	—
267	C₂×#97	—	38	1	no	—
268	C₂×C₄×C₈	—	38	1	no	—
269	#384	—	38	1	no	—
270	#384	—	38	1	no	—
271	#384	—	38	2	no	—
272	#343	—	2	2	no	—
273	#343	—	38	2	no	—
274	#343	—	38	2	no	—
275	#343	—	38	2	no	—
276	C₂×C₁₉	—	2	1	no	—
277	C₂×C₁₉	—	2	1	no	—
278	C₂×C₁₉	—	2	1	no	—
279	C₂×C₁₉	—	2	1	no	—
280	C₂×C₁₉	C₄⋊#95	1	1	yes	characteristic
281	C₂×C₁₉	C₂×#343	1	2	yes	—
282	C₂×C₁₉	#1965	1	1	yes	characteristic
283	C₂×C₁₉	#1966	1	1	yes	characteristic
284	C₂×C₁₉	#1997	1	2	yes	—
285	C₂³×C₄	—	19	2	no	—
286	C₂³×C₄	—	19	2	no	—
287	C₂³×C₄	C₄×D₁₉	1	2	yes	—
288	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	2	1	no	—
293	C₂×M₁₆	—	2	1	no	—
294	C₂×M₁₆	—	2	1	no	—
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	19	2	no	—
298	C₂×M₁₆	—	19	2	no	—
299	C₂×M₁₆	—	19	2	no	—
300	C₂×M₁₆	—	19	2	no	—
301	C₂×M₁₆	—	38	1	no	—
302	C₂×M₁₆	—	38	1	no	—
303	C₂×M₁₆	—	38	1	no	—
304	C₂×M₁₆	—	38	1	no	—
305	C₂×M₁₆	—	38	1	no	—
306	C₂×M₁₆	—	38	1	no	—
307	C₂×M₁₆	—	38	1	no	—
308	C₂×M₁₆	—	38	1	no	—
309	C₂×M₁₆	Dic₃₈	1	2	yes	—
310	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
311	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
312	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	38	1	no	—
316	C₂²×C₈	—	38	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	38	4	no	—
324	C₂×C₄⋊C₄	—	38	4	no	—
325	C₂×C₄⋊C₄	—	38	1	no	—
326	C₂×C₄⋊C₄	—	38	1	no	—
327	C₂×C₄⋊C₄	—	38	1	no	—
328	C₂×C₄⋊C₄	—	38	1	no	—
329	C₂×C₄⋊C₄	—	38	1	no	—
330	C₂×C₄⋊C₄	—	38	1	no	—
331	C₂×C₄⋊C₄	—	76	8	no	—
332	C₂×C₄²	—	19	2	no	—
333	C₂×C₄²	—	19	2	no	—
334	C₂×C₄²	—	19	1	no	—
335	C₂×C₄²	—	19	1	no	—
336	C₂×C₄²	—	19	2	no	—
337	C₂×C₄²	—	19	2	no	—
338	C₂×C₄²	—	19	2	no	—
339	C₄⋊C₈	—	38	8	no	—
340	#97	—	38	4	no	—
341	C₄×C₈	—	38	4	no	—
342	C₁₉	#10857	1	1	yes	characteristic, complemented, Sylow
343	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	19	2	no	—
349	C₂²×C₄	—	19	4	no	—
350	C₂²×C₄	—	19	2	no	—
351	C₂²×C₄	—	19	4	no	—
352	C₂²×C₄	—	38	4	no	—
353	C₂²×C₄	—	38	4	no	—
354	C₂²×C₄	—	38	2	no	—
355	C₂²×C₄	—	38	2	no	—
356	C₂²×C₄	—	38	2	no	—
357	C₂²×C₄	—	76	4	no	—
358	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
361	C₂²×C₄	#64541	1	1	yes	characteristic
362	C₂²×C₄	#64541	1	1	yes	characteristic
363	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
364	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
365	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
366	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
367	C₂²×C₄	#64543	1	1	yes	characteristic
368	C₂²×C₄	#64543	1	1	yes	characteristic
369	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
370	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	—	4	1	no	—
378	M₁₆	—	4	1	no	—
379	M₁₆	—	19	4	no	—
380	M₁₆	—	38	2	no	—
381	M₁₆	—	38	2	no	—
382	M₁₆	—	38	2	no	—
383	M₁₆	—	38	2	no	—
384	M₁₆	—	38	2	no	—
385	M₁₆	—	76	1	no	—
386	M₁₆	—	76	1	no	—
387	M₁₆	Dic₁₉⋊C₄	1	4	yes	complemented
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	1	no	—
393	C₂×C₈	—	4	1	no	—
394	C₂×C₈	—	38	2	no	—
395	C₂×C₈	—	38	2	no	—
396	C₂×C₈	—	38	2	no	—
397	C₂×C₈	—	38	2	no	—
398	C₂×C₈	—	76	1	no	—
399	C₂×C₈	—	76	1	no	—
400	C₄⋊C₄	—	4	1	no	—
401	C₄⋊C₄	—	4	1	no	—
402	C₄⋊C₄	—	4	1	no	—
403	C₄⋊C₄	—	4	1	no	—
404	C₄⋊C₄	—	76	8	no	—
405	C₄⋊C₄	—	76	8	no	—
406	C₄⋊C₄	—	76	1	no	—
407	C₄⋊C₄	—	76	1	no	—
408	C₄⋊C₄	—	76	1	no	—
409	C₄⋊C₄	—	76	1	no	—
410	C₄²	—	19	2	no	—
411	C₄²	—	19	2	no	—
412	C₄²	—	19	4	no	—
413	C₄²	—	19	2	no	—
414	C₄²	—	19	4	no	—
415	C₄²	—	19	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
419	C₂³	C₄²×D₁₉	1	1	yes	characteristic
420	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
421	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
422	C₂³	#10597333	1	1	yes	characteristic
423	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
424	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	19	4	no	—
430	C₂×C₄	—	19	4	no	—
431	C₂×C₄	—	19	4	no	—
432	C₂×C₄	—	19	4	no	—
433	C₂×C₄	—	38	8	no	—
434	C₂×C₄	—	38	8	no	—
435	C₂×C₄	—	38	2	no	—
436	C₂×C₄	—	38	2	no	—
437	C₂×C₄	—	76	2	no	—
438	C₂×C₄	—	76	4	no	—
439	C₂×C₄	—	152	2	no	—
440	C₂×C₄	—	152	2	no	—
441	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
442	C₂×C₄	#10597318	1	1	yes	characteristic
443	C₂×C₄	#10597323	1	1	yes	characteristic
444	C₂×C₄	#10597324	1	1	yes	characteristic
445	C₂×C₄	#10597324	1	1	yes	characteristic
446	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
447	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
448	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
449	C₂×C₄	#10597330	1	1	yes	characteristic
450	C₂×C₄	#10597330	1	1	yes	characteristic
451	C₂×C₄	#10597331	1	1	yes	characteristic
452	C₂×C₄	#10597331	1	1	yes	characteristic
453	C₂×C₄	#10597333	1	1	yes	characteristic
454	C₂×C₄	#10597334	1	1	yes	characteristic
455	C₂×C₄	#10597334	1	1	yes	characteristic
456	C₂×C₄	#10597335	1	1	yes	characteristic
457	C₂×C₄	#10597335	1	1	yes	characteristic
458	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
459	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
460	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
461	C₂×C₄	#10597342	1	1	yes	characteristic
462	C₂×C₄	#10597342	1	1	yes	characteristic
463	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
464	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
465	C₂×C₄	#10597385	1	1	yes	characteristic
466	C₂×C₄	#10597385	1	1	yes	characteristic
467	C₂×C₄	#10597386	1	1	yes	characteristic
468	C₂×C₄	#10597390	1	1	yes	characteristic
469	C₈	—	2	4	no	—
470	C₈	—	4	2	no	—
471	C₈	—	38	4	no	—
472	C₈	—	76	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	#95×D₁₉	1	1	yes	characteristic
482	C₂²	#11926395	1	1	yes	characteristic
483	C₂²	C₄×Dic₁₉⋊C₄	1	1	yes	characteristic
484	C₂²	#11926439	1	1	yes	characteristic
485	C₂²	#11926441	1	1	yes	characteristic
486	C₂²	#11926444	1	1	yes	characteristic
487	C₂²	#11926448	1	1	yes	characteristic
488	C₂²	#100×D₁₉	1	2	yes	—
489	C₂²	#101×D₁₉	1	2	yes	—
490	C₄	—	8	2	no	—
491	C₄	—	19	8	no	—
492	C₄	—	38	4	no	—
493	C₄	—	152	2	no	—
494	C₄	#11926402	1	1	yes	characteristic
495	C₄	#11926403	1	1	yes	characteristic
496	C₄	#11926408	1	1	yes	characteristic
497	C₄	#11926413	1	1	yes	characteristic
498	C₄	#11926439	1	1	yes	characteristic
499	C₄	#11926441	1	1	yes	characteristic
500	C₄	#11926444	1	1	yes	characteristic
501	C₄	#11926448	1	1	yes	characteristic
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	2	1	no	—
506	C₂	Dic₁₉⋊#95	1	1	yes	characteristic
507	C₂	D₁₉×#343	1	2	yes	—
508	C₂	#14564473	1	1	yes	characteristic
509	C₂	#14564477	1	1	yes	characteristic
510	C₂	#14564622	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator	C₂³×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#343	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#343	D₁₉
hypocenter	C₁₉	#10857
LCS	G ▷ C₂³×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
14. #11926567	C₄	semidirect
17. M₁₆×Dic₁₉	C₄	semidirect
123. M₁₆×C₁₉	C₄⋊C₄	semidirect
153. #64520	C₄⋊C₄	semidirect
253. Dic₁₉	#343	semidirect
342. C₁₉	#10857	semidirect
387. M₁₆	Dic₁₉⋊C₄	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×M₁₆×Dic₁₉	2
C₂×#11926413	2
C₂×#11926313	2
C₂×#11926312	2
C₂×C₁₉×#343	2
#10857	19