Subgroups — #18088203

Order 4864.

850 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#117×Dic₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926304	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
5	#14563328	C₂	1	1	yes	maximal, characteristic
6	C₄×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×Dic₁₉	C₄	1	2	yes	complemented
13	C₄⋊C₄×Dic₁₉	C₄	1	2	yes	complemented
14	C₂²⋊C₄×Dic₁₉	—	2	2	no	—
15	#11926390	—	2	1	no	—
16	C₂×C₁₉⋊#95	—	2	2	no	—
17	C₄²×Dic₁₉	—	2	1	no	—
18	#11926305	—	2	2	no	—
19	#11926304	—	2	2	no	—
20	#11926303	C₄	1	4	yes	complemented
21	#11926298	—	2	1	no	—
22	#11926298	—	2	1	no	—
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#339	C₄	1	4	yes	complemented
27	C₂³×C₄×C₁₉	—	2	1	no	—
28	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
29	C₂³×Dic₁₉	—	2	1	no	—
30	C₂³×Dic₁₉	D₄	1	2	yes	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	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	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₁₉×#117	—	2	1	no	—
39	C₁₉×#117	—	2	1	no	—
40	C₁₉×#117	C₂×C₄	1	2	yes	—
41	C₁₉×#117	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	—	2	1	no	—
48	C₂×C₄²×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
53	#10597372	—	2	1	no	—
54	#10597372	—	2	1	no	—
55	#10597372	D₄	1	2	yes	—
56	#10597372	Q₈	1	2	yes	—
57	C₂×C₄⋊Dic₁₉	C₂×C₄	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	—	2	1	no	—
64	C₂×C₄×Dic₁₉	—	2	1	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	2	no	—
69	C₂×C₄×Dic₁₉	—	2	2	no	—
70	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
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	C₂×C₄	1	2	yes	—
80	C₂²×C₁₉⋊C₈	—	2	1	no	—
81	C₁₉⋊#95	—	2	8	no	—
82	C₁₉⋊#95	—	2	2	no	—
83	C₁₉⋊#95	—	2	2	no	—
84	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	—	2	4	no	—
86	C₂²×C₄×C₁₉	—	2	1	no	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	4	2	no	—
90	C₂²×C₄×C₁₉	—	4	1	no	—
91	C₂²×C₄×C₁₉	—	4	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×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	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	4	no	—
107	C₂²×Dic₁₉	—	2	2	no	—
108	C₂²×Dic₁₉	—	2	2	no	—
109	C₂²×Dic₁₉	—	2	2	no	—
110	C₂²×Dic₁₉	—	2	2	no	—
111	C₂²×Dic₁₉	—	2	4	no	—
112	C₂²×Dic₁₉	—	4	2	no	—
113	C₂²×Dic₁₉	—	4	2	no	—
114	C₂²×Dic₁₉	—	4	1	no	—
115	C₂²×Dic₁₉	—	4	1	no	—
116	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
117	C₂²×Dic₁₉	C₂²⋊C₄	1	2	yes	—
118	M₁₆×C₁₉	—	2	2	no	—
119	M₁₆×C₁₉	—	2	2	no	—
120	M₁₆×C₁₉	—	4	1	no	—
121	M₁₆×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	2	2	no	—
123	C₂×C₈×C₁₉	—	4	1	no	—
124	C₂×C₈×C₁₉	—	4	1	no	—
125	C₄⋊C₄×C₁₉	—	2	1	no	—
126	C₄⋊C₄×C₁₉	—	2	1	no	—
127	C₄⋊C₄×C₁₉	C₄²	1	2	yes	—
128	C₄⋊C₄×C₁₉	C₄²	1	2	yes	—
129	C₂²⋊C₄×C₁₉	—	2	2	no	—
130	C₂²⋊C₄×C₁₉	—	2	2	no	—
131	C₄²×C₁₉	—	2	2	no	—
132	C₄²×C₁₉	—	2	2	no	—
133	C₄²×C₁₉	—	2	2	no	—
134	C₄²×C₁₉	—	2	2	no	—
135	C₄²×C₁₉	—	4	1	no	—
136	C₄²×C₁₉	—	4	1	no	—
137	C₂²⋊Dic₁₉	—	2	2	no	—
138	C₂²⋊Dic₁₉	—	2	2	no	—
139	C₄⋊Dic₁₉	—	2	2	no	—
140	C₄⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
141	C₄×Dic₁₉	—	2	2	no	—
142	C₄×Dic₁₉	—	2	2	no	—
143	C₄×Dic₁₉	—	2	2	no	—
144	C₄×Dic₁₉	—	2	2	no	—
145	C₄×Dic₁₉	—	2	1	no	—
146	C₄×Dic₁₉	—	2	1	no	—
147	C₄×Dic₁₉	—	2	1	no	—
148	C₄×Dic₁₉	—	2	1	no	—
149	C₄×Dic₁₉	—	2	2	no	—
150	C₄×Dic₁₉	—	2	2	no	—
151	C₄×Dic₁₉	—	4	4	no	—
152	C₄×Dic₁₉	—	4	1	no	—
153	C₄×Dic₁₉	—	4	1	no	—
154	C₄×Dic₁₉	—	4	4	no	—
155	#64520	—	2	2	no	—
156	#64520	—	2	2	no	—
157	#64520	—	4	1	no	—
158	#64520	—	4	1	no	—
159	C₂×C₁₉⋊C₈	—	2	2	no	—
160	C₂×C₁₉⋊C₈	—	4	1	no	—
161	C₂×C₁₉⋊C₈	—	4	1	no	—
162	#10808	—	19	1	no	maximal, Sylow
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	C₂×C₂²⋊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	#121	1	1	yes	characteristic
169	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂³×C₁₉	#123	1	1	yes	characteristic
171	C₂³×C₁₉	#123	1	1	yes	characteristic
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	2	no	—
175	C₂×C₄×C₁₉	—	4	4	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	2	no	—
179	C₂×C₄×C₁₉	—	4	2	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₄×Q₈	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	#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	#124	1	1	yes	characteristic
203	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
205	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
206	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
207	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
208	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
209	C₂×Dic₁₉	—	2	2	no	—
210	C₂×Dic₁₉	—	2	2	no	—
211	C₂×Dic₁₉	—	2	4	no	—
212	C₂×Dic₁₉	—	2	4	no	—
213	C₂×Dic₁₉	—	2	2	no	—
214	C₂×Dic₁₉	—	2	2	no	—
215	C₂×Dic₁₉	—	2	2	no	—
216	C₂×Dic₁₉	—	4	4	no	—
217	C₂×Dic₁₉	—	4	4	no	—
218	C₂×Dic₁₉	—	4	4	no	—
219	C₂×Dic₁₉	—	4	4	no	—
220	C₂×Dic₁₉	—	4	2	no	—
221	C₂×Dic₁₉	—	4	2	no	—
222	C₂×Dic₁₉	—	4	2	no	—
223	C₂×Dic₁₉	—	4	2	no	—
224	C₂×Dic₁₉	#104	1	4	yes	—
225	C₈×C₁₉	—	4	2	no	—
226	C₁₉⋊C₈	—	4	2	no	—
227	C₄×#117	—	19	1	no	—
228	C₂×#339	—	19	1	no	—
229	C₂×#339	—	19	1	no	—
230	C₂×#339	—	19	1	no	—
231	C₂×#339	D₁₉	1	1	yes	characteristic
232	#1728	—	19	1	no	—
233	C₄×#95	—	19	1	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	2	2	no	—
236	C₂²×C₁₉	—	2	2	no	—
237	C₂²×C₁₉	—	2	2	no	—
238	C₂²×C₁₉	—	2	1	no	—
239	C₂²×C₁₉	—	2	1	no	—
240	C₂²×C₁₉	—	2	1	no	—
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
243	C₂²×C₁₉	#380	1	1	yes	characteristic
244	C₂²×C₁₉	#381	1	1	yes	characteristic
245	C₂²×C₁₉	#387	1	1	yes	characteristic
246	C₂²×C₁₉	#387	1	1	yes	characteristic
247	C₂²×C₁₉	#388	1	1	yes	characteristic
248	C₂²×C₁₉	#388	1	1	yes	characteristic
249	C₂²×C₁₉	C₂×#104	1	2	yes	—
250	C₂²×C₁₉	#421	1	2	yes	—
251	C₄×C₁₉	—	4	4	no	—
252	C₄×C₁₉	—	4	2	no	—
253	C₄×C₁₉	—	4	2	no	—
254	C₄×C₁₉	#376	1	1	yes	characteristic
255	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
256	C₄×C₁₉	#382	1	1	yes	characteristic
257	C₄×C₁₉	#383	1	1	yes	characteristic
258	C₄×C₁₉	#387	1	1	yes	characteristic
259	C₄×C₁₉	#387	1	1	yes	characteristic
260	C₄×C₁₉	#388	1	1	yes	characteristic
261	C₄×C₁₉	#388	1	1	yes	characteristic
262	Dic₁₉	—	2	4	no	—
263	Dic₁₉	—	4	4	no	—
264	Dic₁₉	—	4	4	no	—
265	Dic₁₉	—	4	2	no	—
266	C₂²×M₁₆	—	19	1	no	—
267	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
268	C₂×#117	—	19	1	no	—
269	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
270	C₂²×C₄²	—	19	1	no	—
271	C₂²×C₄²	—	19	1	no	—
272	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
273	C₄×C₄⋊C₄	—	19	2	no	—
274	C₄×C₄⋊C₄	—	19	2	no	—
275	C₄×C₂²⋊C₄	—	38	2	no	—
276	#376	—	38	1	no	—
277	C₂×#95	—	38	2	no	—
278	C₄³	—	38	1	no	—
279	#339	—	19	4	no	—
280	#339	—	38	2	no	—
281	#339	—	38	2	no	—
282	#339	Dic₁₉	1	4	yes	complemented
283	#336	—	38	1	no	—
284	#336	—	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	#1434	1	1	yes	characteristic
290	C₂×C₁₉	C₄×#104	1	1	yes	characteristic
291	C₂×C₁₉	#1759	1	1	yes	characteristic
292	C₂×C₁₉	#1806	1	2	yes	—
293	C₂×C₁₉	#1826	1	2	yes	—
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	—	19	2	no	—
296	C₂³×C₄	—	38	1	no	—
297	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
298	C₂×M₁₆	—	2	1	no	—
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	—	19	2	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	C₂×Dic₁₉	1	2	yes	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	38	1	no	—
312	#117	—	2	1	no	—
313	#117	—	2	1	no	—
314	#117	—	19	2	no	—
315	#117	—	19	2	no	—
316	#117	—	38	1	no	—
317	#117	—	38	1	no	—
318	#117	C₄×D₁₉	1	2	yes	—
319	#117	C₂×Dic₁₉	1	2	yes	—
320	C₂×C₄⋊C₄	—	19	2	no	—
321	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	38	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	1	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	19	2	no	—
332	C₂×C₄²	—	19	1	no	—
333	C₂×C₄²	—	19	1	no	—
334	C₂×C₄²	—	19	2	no	—
335	C₂×C₄²	—	38	1	no	—
336	C₂×C₄²	—	38	1	no	—
337	C₂×C₄²	—	38	1	no	—
338	C₂×C₄²	—	38	1	no	—
339	C₂×C₄²	—	38	1	no	—
340	C₂×C₄²	—	38	1	no	—
341	C₂×C₄²	—	38	1	no	—
342	C₂×C₄²	—	38	1	no	—
343	C₂×C₄²	—	38	1	no	—
344	C₂×C₄²	—	38	2	no	—
345	C₂×C₄²	—	38	2	no	—
346	C₂×C₄²	—	38	1	no	—
347	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
348	#95	—	38	2	no	—
349	#95	—	38	2	no	—
350	#95	—	38	8	no	—
351	C₁₉	#10808	1	1	yes	characteristic, complemented, Sylow
352	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	19	2	no	—
361	C₂²×C₄	—	19	2	no	—
362	C₂²×C₄	—	38	4	no	—
363	C₂²×C₄	—	38	4	no	—
364	C₂²×C₄	—	38	2	no	—
365	C₂²×C₄	—	38	2	no	—
366	C₂²×C₄	—	38	2	no	—
367	C₂²×C₄	—	38	2	no	—
368	C₂²×C₄	—	76	2	no	—
369	C₂²×C₄	—	76	2	no	—
370	C₂²×C₄	—	76	1	no	—
371	C₂²×C₄	—	76	1	no	—
372	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
374	C₂²×C₄	#64541	1	1	yes	characteristic
375	C₂²×C₄	#64541	1	1	yes	characteristic
376	C₂²×C₄	#64541	1	1	yes	characteristic
377	C₂²×C₄	#64541	1	1	yes	characteristic
378	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
379	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
380	C₂²×C₄	#64543	1	1	yes	characteristic
381	C₂²×C₄	#64543	1	1	yes	characteristic
382	C₂²×C₄	#64543	1	1	yes	characteristic
383	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
384	C₂²×C₄	#64545	1	1	yes	characteristic
385	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	4	1	no	—
389	M₁₆	—	4	1	no	—
390	M₁₆	—	38	2	no	—
391	M₁₆	—	38	2	no	—
392	M₁₆	—	76	1	no	—
393	M₁₆	—	76	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	4	1	no	—
396	C₂×C₈	—	4	1	no	—
397	C₂×C₈	—	38	2	no	—
398	C₂×C₈	—	76	1	no	—
399	C₂×C₈	—	76	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	19	4	no	—
403	C₄⋊C₄	—	38	2	no	—
404	C₄⋊C₄	C₄×Dic₁₉	1	2	yes	—
405	C₄⋊C₄	C₄×Dic₁₉	1	2	yes	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	38	2	no	—
409	C₂²⋊C₄	—	38	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	4	1	no	—
415	C₄²	—	4	1	no	—
416	C₄²	—	38	2	no	—
417	C₄²	—	38	1	no	—
418	C₄²	—	38	1	no	—
419	C₄²	—	38	2	no	—
420	C₄²	—	38	2	no	—
421	C₄²	—	38	1	no	—
422	C₄²	—	38	1	no	—
423	C₄²	—	38	2	no	—
424	C₄²	—	38	2	no	—
425	C₄²	—	38	2	no	—
426	C₄²	—	76	4	no	—
427	C₄²	—	76	4	no	—
428	C₄²	—	76	1	no	—
429	C₄²	—	76	1	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
433	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
434	C₂³	#10597329	1	1	yes	characteristic
435	C₂³	#10597330	1	1	yes	characteristic
436	C₂³	#10597340	1	1	yes	characteristic
437	C₂³	#10597342	1	1	yes	characteristic
438	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	19	4	no	—
449	C₂×C₄	—	38	2	no	—
450	C₂×C₄	—	38	2	no	—
451	C₂×C₄	—	38	4	no	—
452	C₂×C₄	—	38	2	no	—
453	C₂×C₄	—	38	2	no	—
454	C₂×C₄	—	38	4	no	—
455	C₂×C₄	—	38	2	no	—
456	C₂×C₄	—	76	4	no	—
457	C₂×C₄	—	76	4	no	—
458	C₂×C₄	—	76	4	no	—
459	C₂×C₄	—	76	2	no	—
460	C₂×C₄	—	76	4	no	—
461	C₂×C₄	—	76	2	no	—
462	C₂×C₄	—	76	2	no	—
463	C₂×C₄	—	76	2	no	—
464	C₂×C₄	#10597318	1	1	yes	characteristic
465	C₂×C₄	#10597318	1	1	yes	characteristic
466	C₂×C₄	#10597318	1	1	yes	characteristic
467	C₂×C₄	#10597318	1	1	yes	characteristic
468	C₂×C₄	#10597323	1	1	yes	characteristic
469	C₂×C₄	#10597325	1	1	yes	characteristic
470	C₂×C₄	#10597325	1	1	yes	characteristic
471	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
472	C₂×C₄	#10597329	1	1	yes	characteristic
473	C₂×C₄	#10597330	1	1	yes	characteristic
474	C₂×C₄	#10597331	1	1	yes	characteristic
475	C₂×C₄	#10597331	1	1	yes	characteristic
476	C₂×C₄	#10597333	1	1	yes	characteristic
477	C₂×C₄	#10597335	1	1	yes	characteristic
478	C₂×C₄	#10597335	1	1	yes	characteristic
479	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
480	C₂×C₄	#10597338	1	1	yes	characteristic
481	C₂×C₄	#10597339	1	1	yes	characteristic
482	C₂×C₄	#10597340	1	1	yes	characteristic
483	C₂×C₄	#10597342	1	1	yes	characteristic
484	C₂×C₄	#10597344	1	1	yes	characteristic
485	C₂×C₄	#10597344	1	1	yes	characteristic
486	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
487	C₂×C₄	#10597372	1	1	yes	characteristic
488	C₂×C₄	#10597372	1	1	yes	characteristic
489	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
490	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
491	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
492	C₈	—	4	2	no	—
493	C₈	—	76	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
503	C₂²	#11926403	1	1	yes	characteristic
504	C₂²	#11926406	1	1	yes	characteristic
505	C₂²	#11926426	1	1	yes	characteristic
506	C₂²	#11926430	1	1	yes	characteristic
507	C₂²	#11926433	1	1	yes	characteristic
508	C₂²	#11926437	1	1	yes	characteristic
509	C₂²	#104×D₁₉	1	2	yes	—
510	C₂²	#11926559	1	2	yes	—
511	C₄	—	4	4	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	38	4	no	—
515	C₄	—	76	4	no	—
516	C₄	—	76	4	no	—
517	C₄	—	76	2	no	—
518	C₄	#11926390	1	1	yes	characteristic
519	C₄	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
520	C₄	#11926408	1	1	yes	characteristic
521	C₄	#11926411	1	1	yes	characteristic
522	C₄	#11926426	1	1	yes	characteristic
523	C₄	#11926430	1	1	yes	characteristic
524	C₄	#11926433	1	1	yes	characteristic
525	C₄	#11926437	1	1	yes	characteristic
526	C₂	—	2	1	no	—
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	#14561860	1	1	yes	characteristic
531	C₂	#104×Dic₁₉	1	1	yes	characteristic
532	C₂	#14563447	1	1	yes	characteristic
533	C₂	#14563654	1	2	yes	—
534	C₂	#14563733	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#339	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#339	D₁₉
hypocenter	C₁₉	#10808
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
12. C₄⋊C₄×Dic₁₉	C₄	semidirect
13. C₄⋊C₄×Dic₁₉	C₄	semidirect
20. #11926303	C₄	semidirect
26. C₁₉×#339	C₄	semidirect
282. #339	Dic₁₉	semidirect
351. C₁₉	#10808	semidirect

Maximal subgroups

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

subgroup	index
#117×Dic₁₉	2
C₂×#11926305	2
C₂×#11926304	2
C₂×#11926303	2
#14563328	2
C₄×C₁₉⋊#95	2
C₂×C₁₉×#339	2
#10808	19